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On the paramodularity
of typical abelian surfaces
Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaría, John Voight and David S. Yuen |
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Vol. 13 (2019), No. 5, 1145–1195
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Abstract |
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Generalizing the method of Faltings–Serre, we rigorously verify that certain abelian surfaces without extra endomorphisms are paramodular. To compute the required Hecke eigenvalues, we develop a method of specialization of Siegel paramodular forms to modular curves. An errata, with an appendix by J.-P. Serre, was submitted on 9 November 2020 and posted online on 11 November 2020. |
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Keywords
abelian surfaces, Siegel modular forms, computation
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Mathematical Subject Classification 2010
Primary: 11F46
Secondary: 11Y40
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Supplementary material |
Milestones
Received: 6 July 2018
Revised: 24 January 2019
Accepted: 2 April 2019
Published: 12 July 2019
Correction posted: 11 November 2020 |
Authors |
| Armand Brumer | |
| Department of Mathematics Fordham University Bronx, NY United States |
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| Ariel Pacetti | |
| FAMAF-CIEM Universidad Nacional de Córdoba Argentina |
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| Cris Poor | |
| Department of Mathematics Fordham University Bronx, NY United States |
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| Gonzalo Tornaría | |
| Centro de Matemática Universidad de la República Montevideo Uruguay |
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| John Voight | |
| Department of Mathematics Dartmouth College Hanover, NH United States |
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| David S. Yuen | |
| Department of Mathematics University of Hawaii Honolulu, HI United States |
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