Examples of abelian surfaces with everywhere good reduction
arXiv:1309.3821 · doi:10.1007/s00208-015-1252-6
Abstract
We describe several explicit examples of simple abelian surfaces over real quadratic fields with real multiplication and everywhere good reduction. These examples provide evidence for the Eichler-Shimura conjecture for Hilbert modular forms over a real quadratic field. Several of the examples also support a conjecture of Brumer and Kramer on abelian varieties associated to Siegel modular forms with paramodular level structures.
26 pages. Final version (to appear in Mathematische Annalen)