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Non-abelian p-adic L-functions and Eisenstein series of unitary groups -The CM method

Bouganis, A.

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Abstract

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”.

Citation

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 Mar 28, 2024
Journal Annales de l'Institut Fourier
Print ISSN 0373-0956
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.

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