Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration
We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proo...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Groechenig, Michael [verfasserIn] Wyss, Dimitri [verfasserIn] Ziegler, Paul [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Ausgabe: |
Published: 01 April 2020 |
| Anmerkung: |
Last seen: 11.05.2022 |
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| Übergeordnetes Werk: |
Enthalten in: Inventiones mathematicae - Berlin : Springer, 1966, Volume 221(2020), Issue 2, pp. 505-596 |
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| Übergeordnetes Werk: |
volume:221 ; year:2020 ; number:2 ; pages:505-596 |
| Links: |
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| DOI / URN: |
10.1007/s00222-020-00957-8 |
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| Katalog-ID: |
1801375259 |
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| 245 | 1 | 0 | |a Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration |
| 250 | |a Published: 01 April 2020 | ||
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| 520 | |a We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy-Schiffmann in the coprime case. | ||
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10.1007/s00222-020-00957-8 doi (DE-627)1801375259 (DE-599)KXP1801375259 DE-627 ger DE-627 rda eng Groechenig, Michael verfasserin (DE-588)1257257412 (DE-627)1801375763 aut Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration Published: 01 April 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 11.05.2022 We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy-Schiffmann in the coprime case. Wyss, Dimitri verfasserin (DE-588)1157042325 (DE-627)1020042354 (DE-576)502598093 aut Ziegler, Paul verfasserin (DE-588)1257257927 (DE-627)1801376468 aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 Volume 221(2020), Issue 2, pp. 505-596 Online-Ressource (DE-627)235503525 (DE-600)1398341-6 (DE-576)061936049 1432-1297 nnns volume:221 year:2020 number:2 pages:505-596 https://doi.org/10.1007/s00222-020-00957-8 Verlag Resolving-System Full text at Publisher kostenfrei GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 221 2020 2 505-596 Volume 221(2020), Issue 2, pp. 505-596 2088 01 DE-Frei3c 4131905663 00 --%%-- --%%-- --%%-- n Funding text: A substantial part of the research described in this paper was conducted during a “Research in Pairs” stay at the Mathematisches Forschungsinstitut Oberwolfach. l01 11-05-22 2403 01 DE-LFER 4143610981 00 --%%-- --%%-- n --%%-- l01 07-06-22 2403 01 DE-LFER https://doi.org/10.1007/s00222-020-00957-8 |
| spelling |
10.1007/s00222-020-00957-8 doi (DE-627)1801375259 (DE-599)KXP1801375259 DE-627 ger DE-627 rda eng Groechenig, Michael verfasserin (DE-588)1257257412 (DE-627)1801375763 aut Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration Published: 01 April 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 11.05.2022 We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy-Schiffmann in the coprime case. Wyss, Dimitri verfasserin (DE-588)1157042325 (DE-627)1020042354 (DE-576)502598093 aut Ziegler, Paul verfasserin (DE-588)1257257927 (DE-627)1801376468 aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 Volume 221(2020), Issue 2, pp. 505-596 Online-Ressource (DE-627)235503525 (DE-600)1398341-6 (DE-576)061936049 1432-1297 nnns volume:221 year:2020 number:2 pages:505-596 https://doi.org/10.1007/s00222-020-00957-8 Verlag Resolving-System Full text at Publisher kostenfrei GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 221 2020 2 505-596 Volume 221(2020), Issue 2, pp. 505-596 2088 01 DE-Frei3c 4131905663 00 --%%-- --%%-- --%%-- n Funding text: A substantial part of the research described in this paper was conducted during a “Research in Pairs” stay at the Mathematisches Forschungsinstitut Oberwolfach. l01 11-05-22 2403 01 DE-LFER 4143610981 00 --%%-- --%%-- n --%%-- l01 07-06-22 2403 01 DE-LFER https://doi.org/10.1007/s00222-020-00957-8 |
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10.1007/s00222-020-00957-8 doi (DE-627)1801375259 (DE-599)KXP1801375259 DE-627 ger DE-627 rda eng Groechenig, Michael verfasserin (DE-588)1257257412 (DE-627)1801375763 aut Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration Published: 01 April 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 11.05.2022 We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy-Schiffmann in the coprime case. Wyss, Dimitri verfasserin (DE-588)1157042325 (DE-627)1020042354 (DE-576)502598093 aut Ziegler, Paul verfasserin (DE-588)1257257927 (DE-627)1801376468 aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 Volume 221(2020), Issue 2, pp. 505-596 Online-Ressource (DE-627)235503525 (DE-600)1398341-6 (DE-576)061936049 1432-1297 nnns volume:221 year:2020 number:2 pages:505-596 https://doi.org/10.1007/s00222-020-00957-8 Verlag Resolving-System Full text at Publisher kostenfrei GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 221 2020 2 505-596 Volume 221(2020), Issue 2, pp. 505-596 2088 01 DE-Frei3c 4131905663 00 --%%-- --%%-- --%%-- n Funding text: A substantial part of the research described in this paper was conducted during a “Research in Pairs” stay at the Mathematisches Forschungsinstitut Oberwolfach. l01 11-05-22 2403 01 DE-LFER 4143610981 00 --%%-- --%%-- n --%%-- l01 07-06-22 2403 01 DE-LFER https://doi.org/10.1007/s00222-020-00957-8 |
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10.1007/s00222-020-00957-8 doi (DE-627)1801375259 (DE-599)KXP1801375259 DE-627 ger DE-627 rda eng Groechenig, Michael verfasserin (DE-588)1257257412 (DE-627)1801375763 aut Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration Published: 01 April 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 11.05.2022 We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy-Schiffmann in the coprime case. Wyss, Dimitri verfasserin (DE-588)1157042325 (DE-627)1020042354 (DE-576)502598093 aut Ziegler, Paul verfasserin (DE-588)1257257927 (DE-627)1801376468 aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 Volume 221(2020), Issue 2, pp. 505-596 Online-Ressource (DE-627)235503525 (DE-600)1398341-6 (DE-576)061936049 1432-1297 nnns volume:221 year:2020 number:2 pages:505-596 https://doi.org/10.1007/s00222-020-00957-8 Verlag Resolving-System Full text at Publisher kostenfrei GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 221 2020 2 505-596 Volume 221(2020), Issue 2, pp. 505-596 2088 01 DE-Frei3c 4131905663 00 --%%-- --%%-- --%%-- n Funding text: A substantial part of the research described in this paper was conducted during a “Research in Pairs” stay at the Mathematisches Forschungsinstitut Oberwolfach. l01 11-05-22 2403 01 DE-LFER 4143610981 00 --%%-- --%%-- n --%%-- l01 07-06-22 2403 01 DE-LFER https://doi.org/10.1007/s00222-020-00957-8 |
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10.1007/s00222-020-00957-8 doi (DE-627)1801375259 (DE-599)KXP1801375259 DE-627 ger DE-627 rda eng Groechenig, Michael verfasserin (DE-588)1257257412 (DE-627)1801375763 aut Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration Published: 01 April 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 11.05.2022 We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy-Schiffmann in the coprime case. Wyss, Dimitri verfasserin (DE-588)1157042325 (DE-627)1020042354 (DE-576)502598093 aut Ziegler, Paul verfasserin (DE-588)1257257927 (DE-627)1801376468 aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 Volume 221(2020), Issue 2, pp. 505-596 Online-Ressource (DE-627)235503525 (DE-600)1398341-6 (DE-576)061936049 1432-1297 nnns volume:221 year:2020 number:2 pages:505-596 https://doi.org/10.1007/s00222-020-00957-8 Verlag Resolving-System Full text at Publisher kostenfrei GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 221 2020 2 505-596 Volume 221(2020), Issue 2, pp. 505-596 2088 01 DE-Frei3c 4131905663 00 --%%-- --%%-- --%%-- n Funding text: A substantial part of the research described in this paper was conducted during a “Research in Pairs” stay at the Mathematisches Forschungsinstitut Oberwolfach. l01 11-05-22 2403 01 DE-LFER 4143610981 00 --%%-- --%%-- n --%%-- l01 07-06-22 2403 01 DE-LFER https://doi.org/10.1007/s00222-020-00957-8 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">1801375259</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240224111913.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220511s2020 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00222-020-00957-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)1801375259</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)KXP1801375259</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Groechenig, Michael</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(DE-588)1257257412</subfield><subfield code="0">(DE-627)1801375763</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Published: 01 April 2020</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Last seen: 11.05.2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. 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mirror symmetry for moduli spaces of higgs bundles via p-adic integration |
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Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration |
| abstract |
We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy-Schiffmann in the coprime case. Last seen: 11.05.2022 |
| abstractGer |
We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy-Schiffmann in the coprime case. Last seen: 11.05.2022 |
| abstract_unstemmed |
We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy-Schiffmann in the coprime case. Last seen: 11.05.2022 |
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Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration |
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