Examples of abelian surfaces with everywhere good reduction
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208_2015_Article_1252.pdf
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Author(s)
Dembélé, Lassina
Kumar, Abhinav
Date Issued
July 2015
Journal
Mathematische Annalen
Publisher
Springer Berlin Heidelberg
Citation
Dembélé, Lassina, and Abhinav Kumar. “Examples of Abelian Surfaces with Everywhere Good Reduction.” Math. Ann. 364, no. 3–4 (July 23, 2015): 1365–1392.
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Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00208-015-1252-6
