2025/02/28 by Boxer, George, Calegari, Frank, Gee, Toby +1 · 1 citation
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2502.20645
We prove the modularity of a positive proportion of abelian surfaces over Q. More precisely, we prove the modularity of abelian surfaces which are ordinary at 3 and are 3-distinguished, subject to some assumptions on the 3-torsion representation (a "big image" hypothesis, and a technical hypothesis on the action of a decomposition group at 2). We employ a 2-3 switch and a new classicality theorem (in the style of Lue Pan) for ordinary p-adic Siegel modular forms.