Vol. 13, No. 5, 2019

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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

Vol. 13 (2019), No. 5, 1145–1195
Abstract

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.

Keywords
abelian surfaces, Siegel modular forms, computation
Mathematical Subject Classification 2010
Primary: 11F46
Secondary: 11Y40
Supplementary material

Errata

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
Ariel Pacetti
FAMAF-CIEM
Universidad Nacional de Córdoba
Argentina
Cris Poor
Department of Mathematics
Fordham University
Bronx, NY
United States
Gonzalo Tornaría
Centro de Matemática
Universidad de la República
Montevideo
Uruguay
John Voight
Department of Mathematics
Dartmouth College
Hanover, NH
United States
David S. Yuen
Department of Mathematics
University of Hawaii
Honolulu, HI
United States