Lei, Antonio, Loeffler, David and Zerbes, Sarah Livia (2018) Euler systems for Hilbert modular surfaces. Forum of Mathematics, Sigma, 6 . e23. doi:10.1017/fms.2018.23

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Abstract

We construct an Euler system—a compatible family of global cohomology classes—for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Bloch and Kato on injectivity of regulator maps holds, this Euler system is nontrivial, and we deduce bounds towards the Iwasawa main conjecture for these Galois representations.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Hilbert modular surfaces, Galois cohomology
Journal or Publication Title:	Forum of Mathematics, Sigma
Publisher:	Cambridge University Press
ISSN:	2050-5094
Official Date:	15 November 2018
Dates:	Date Event 15 November 2018 Available 11 October 2018 Accepted
Volume:	6
Article Number:	e23
DOI:	10.1017/fms.2018.23
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID 05710 [NSERC] Natural Sciences and Engineering Research Council of Canada http://dx.doi.org/10.13039/501100000038 UNSPECIFIED [RS] Royal Society http://dx.doi.org/10.13039/501100000288 Euler Systems and the Birch–Swinnerton- Dyer conjecture European Research Council http://viaf.org/viaf/130022607
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