On the paramodularity of typical abelian surfaces

2018/05/28 by Armand Brumer, Ariel Pacetti, Cris Poor +4
Mathematics · #Abelian group #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Bilinear form #Computer science #Covariant transformation #Discrete mathematics #Eigenvalues and eigenvectors #Elementary abelian group #Endomorphism #Endomorphism ring #Geometry #Hecke operator #Invariant (physics) #Mathematics #Modular design #Modular form #Modulo #Physics #Pure mathematics #Rank of an abelian group #Siegel modular form #math.NT

paper · pdf · doi:10.2140/ant.2019.13.1145

published as Alg. Number Th. 13 (2019) 1145-1195 · 49 pages; proof of Lemma 4.3.6 simplified, still with the new appendix by Serre

openalex publication_date 2019/07/12 · arxiv created 2020/11/19 · arxiv updated 2020/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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.

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