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

Thanasis Bouganis^{[1]}

- [1] Department of Mathematical Sciences Durham University Science Laboratories, South Rd. Durham DH1 3LE (U.K.)

Annales de l’institut Fourier (2014)

- Volume: 64, Issue: 2, page 793-891
- ISSN: 0373-0956

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topBouganis, Thanasis. "Non-abelian $p$-adic $L$-functions and Eisenstein series of unitary groups – The CM method." Annales de l’institut Fourier 64.2 (2014): 793-891. <http://eudml.org/doc/275632>.

@article{Bouganis2014,

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”},

affiliation = {Department of Mathematical Sciences Durham University Science Laboratories, South Rd. Durham DH1 3LE (U.K.)},

author = {Bouganis, Thanasis},

journal = {Annales de l’institut Fourier},

keywords = {($p$-adic) $L$-functions; Eisenstein Series; Unitary Groups; Congruences; ($p$-adic) $L$-functions; Eisenstein series; unitary groups; congruences},

language = {eng},

number = {2},

pages = {793-891},

publisher = {Association des Annales de l’institut Fourier},

title = {Non-abelian $p$-adic $L$-functions and Eisenstein series of unitary groups – The CM method},

url = {http://eudml.org/doc/275632},

volume = {64},

year = {2014},

}

TY - JOUR

AU - Bouganis, Thanasis

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

JO - Annales de l’institut Fourier

PY - 2014

PB - Association des Annales de l’institut Fourier

VL - 64

IS - 2

SP - 793

EP - 891

AB - 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”

LA - eng

KW - ($p$-adic) $L$-functions; Eisenstein Series; Unitary Groups; Congruences; ($p$-adic) $L$-functions; Eisenstein series; unitary groups; congruences

UR - http://eudml.org/doc/275632

ER -

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