Some modular abelian surfaces

Calegari, Frank; Chidambaram, Shiva; Ghitza, Alexandru

doi:10.1090/mcom/3434

Some modular abelian surfaces
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by Frank Calegari, Shiva Chidambaram and Alexandru Ghitza HTML | PDF

Math. Comp. 89 (2020), 387-394 Request permission

Abstract:

In this note, we use the main theorem of Boxer, Calegari, Gee, and Pilloni in Abelian surfaces over totally real fields are potentially modular ( arXiv:1812.09269, 2018) to give explicit examples of modular abelian surfaces $A$ with $\operatorname {End}_{\mathbf {C}} A = \mathbf {Z}$ and $A$ smooth outside $2$, $3$, $5$, and $7$.

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