# Algèbre de Hecke quasi-ordinaire universelle d'un groupe réductif

Abstract : The starting point of this work is the study of a conjecture of type $R\simeq\mathbb(T)$ in the general case of a connected reductive group $G$, defined over $\mathbb(Q)$, admitting a Shimura variety and not necessarily split. The main assumption is the near-ordinarity of automorphic representations and its Galois counterpart. We get, under mild hypotheses, the equality of the Krull dimensions of a universal deformation ring of a nearly-ordinary Galois representation and of a localised nearly-ordinary Hecke algebra. The theory of Bruhat-Tits building is used to study the structure of parabolic Hecke algebras at $p$. From a general control theorem, we deduce, in certain cases, that the universal nearly-ordinary Hecke algebra is finite and torsion free over the Hida-Iwasawa algebra of $G$. This result allows to construct families of nearly-ordinary Hecke eigensystems passing through a given eigensystem.
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https://tel.archives-ouvertes.fr/tel-00005938
Contributor : David Mauger <>
Submitted on : Tuesday, April 20, 2004 - 4:40:18 PM
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• HAL Id : tel-00005938, version 1

### Citation

David Mauger. Algèbre de Hecke quasi-ordinaire universelle d'un groupe réductif. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2000. Français. ⟨tel-00005938⟩

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