Loeffler, David and Zerbes, Sarah Livia (2021) Euler systems with local conditions. In: Iwasawa 2017: Development of Iwasawa Theory — the Centennial of K. Iwasawa's Birth, Tokyo, Japan, 19-28 Jul 2017. Published in: Advanced Studies in Pure Mathematics, 86 doi:10.2969/aspm/08610001 ISSN 0920-1971.

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Abstract

Euler systems are certain compatible families of cohomology classes, which play a key role in studying the arithmetic of Galois representations. We briefly survey the known Euler systems, and recall a standard conjecture of Perrin-Riou predicting what kind of Euler system one should expect for a general Galois representation. Surprisingly, several recent constructions of Euler systems do not seem to fit the predictions of this conjecture, and we formulate a more general conjecture which explains these extra objects. The novel aspect of our conjecture is that it predicts that there should often be Euler systems of several different ranks associated to a given Galois representation, and we describe how we expect these objects to be related.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Galois cohomology
Journal or Publication Title:	Advanced Studies in Pure Mathematics
Publisher:	Mathematical Society of Japan
ISSN:	0920-1971
Editor:	Kurihara, M. and Bannai, K. and Ochiai, T. and Tsuji, T.
Official Date:	12 January 2021
Dates:	Date Event 12 January 2021 Published 10 December 2020 Available 7 January 2019 Accepted
Volume:	86
DOI:	10.2969/aspm/08610001
Status:	Peer Reviewed
Publication Status:	Published
Reuse Statement (publisher, data, author rights):	Papers which appeared in ASPM vol. 86.
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	7 January 2019
Date of first compliant Open Access:	8 January 2019
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID Euler Systems and the Birch–Swinnerton-Dyer conjecture European Research Council http://viaf.org/viaf/130022607 L-functions and Iwasawa theory [RS] Royal Society http://dx.doi.org/10.13039/501100000288 PLP-2014-354 Leverhulme Trust http://dx.doi.org/10.13039/501100000275
Conference Paper Type:	Paper
Title of Event:	Iwasawa 2017: Development of Iwasawa Theory — the Centennial of K. Iwasawa's Birth
Type of Event:	Conference
Location of Event:	Tokyo, Japan
Date(s) of Event:	19-28 Jul 2017
Related URLs:	Organisation Publisher Publisher
Open Access Version:	ArXiv

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