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Euler systems for Hilbert modular surfaces

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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 ISSN 2050-5094 .

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Official URL: https://doi.org/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, Engineering and Medicine > 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:
DateEvent
15 November 2018Available
11 October 2018Accepted
Volume: 6
Article Number: e23
DOI: 10.1017/fms.2018.23
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 15 October 2018
Date of first compliant Open Access: 26 November 2018
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
05710[NSERC] Natural Sciences and Engineering Research Council of Canadahttp://dx.doi.org/10.13039/501100000038
UNSPECIFIED[RS] Royal Societyhttp://dx.doi.org/10.13039/501100000288
Euler Systems and the Birch–Swinnerton- Dyer conjectureEuropean Research Councilhttp://viaf.org/viaf/130022607
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