Professor Athanasios Bouganis athanasios.bouganis@durham.ac.uk
Professor
In this work we prove various cases of the so-called “torsion congruences” between abelian p-adic L-functions that are related to automorphic representations of definite unitary groups. These congruences play a central role in the non-commutative Iwasawa theory as it became clear in the works of Kakde, Ritter and Weiss on the non-abelian Main Conjecture for the Tate motive. We tackle these congruences for a general definite unitary group of n variables and we obtain more explicit results in the special cases of n = 1 and n = 2. In both of these cases we also explain their implications for some particular “motives”, as for example elliptic curves with complex multiplication. Finally we also discuss a new kind of congruences, which we call “average torsion congruences”.
Bouganis, A. (2014). Non-abelian p-adic L-functions and Eisenstein series of unitary groups -The CM method. Annales de l'Institut Fourier, 64(2), 793-891. https://doi.org/10.5802/aif.2866
Journal Article Type | Article |
---|---|
Acceptance Date | Jan 17, 2014 |
Online Publication Date | Dec 2, 2014 |
Publication Date | Jan 1, 2014 |
Deposit Date | Oct 4, 2013 |
Publicly Available Date | Jan 28, 2015 |
Journal | Annales de l'Institut Fourier |
Print ISSN | 0373-0956 |
Electronic ISSN | 1777-5310 |
Publisher | Association des Annales de l'Institut Fourier |
Peer Reviewed | Peer Reviewed |
Volume | 64 |
Issue | 2 |
Pages | 793-891 |
DOI | https://doi.org/10.5802/aif.2866 |
Keywords | p-adic, L-functions, Eisenstein Series, Unitary Groups, Congruences. |
Public URL | https://durham-repository.worktribe.com/output/1468624 |
Accepted Journal Article
(912 Kb)
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