Presentation of an Iwasawa algebra : the case of \Gamma_1 SL(2,Z_p)

Laurent Clozel (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Assume G is a semi-simple Chevalley group, so G(Zp ) ⊂ G(Qp ) is a max- imal compact subgroup. Both the p-adic representation theory of G(Qp ) and non-commutative Iwasawa theory involve the Iwasawa algebra of G(Zp ) or suitable congruence subgroups. It seems to have been assumed that explicit descriptions, by generators and relations, of these algebras were inaccessi- ble. However, it is a general principle that natural ob jects coming from semi-simple (split) groups have explicit presentations. Famous examples are Serre's presentation of the semi-simple algebras and Steinberg's presentation of the Chevalley groups [7, 8]. In this paper we will give a presentation for the Iwasawa algebra of the subgroup of level 1 in S L(2, Z) (p

Domaines: Théorie des nombres [math.NT]

Laurent Clozel. Presentation of an Iwasawa algebra : the case of \Gamma_1 SL(2,Z_p). 2011. ⟨hal-00617986⟩