Vol. 13, No. 5, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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.

Keywords
abelian surfaces, Siegel modular forms, computation
Mathematical Subject Classification 2010
Primary: 11F46
Secondary: 11Y40
Milestones
Received: 6 July 2018
Revised: 24 January 2019
Accepted: 2 April 2019
Published: 12 July 2019
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