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

Bouganis, A.

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: 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