Kings, Guido, Loeffler, David and Zerbes, Sarah Livia (2017) Rankin–Eisenstein classes and explicit reciprocity laws. Cambridge Journal of Mathematics, 5 (1). pp. 1-122. doi:10.4310/CJM.2017.v5.n1.a1 ISSN 2168-0930.

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Abstract

We construct three-variable p-adic families of Galois cohomology classes attached to Rankin convolutions of modular forms, and prove an explicit reciprocity law relating these classes to critical values of L-functions. As a consequence, we prove finiteness results for the Selmer group of an elliptic curve twisted by a 2-dimensional odd irreducible Artin representation when the associated L-value does not vanish.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Number theory, L-functions, Galois cohomology, Iwasawa theory
Journal or Publication Title:	Cambridge Journal of Mathematics
Publisher:	International Press
ISSN:	2168-0930
Official Date:	January 2017
Dates:	Date Event January 2017 Published 7 December 2016 Accepted
Volume:	5
Number:	1
Page Range:	pp. 1-122
DOI:	10.4310/CJM.2017.v5.n1.a1
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	9 December 2016
Date of first compliant Open Access:	15 December 2016
Funder:	Banff International Research Station Workshop on Applications of Iwasawa Algebras, Mathematical sciences research institute Berkeley, Calif
Related URLs:	Publisher

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