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arXiv: 1105.2957

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Modules universels de GL(3) sur un corps p-adique en caractéristique p

Rachel Ollivier 1, 2, Vincent Sécherre 1

(2011-05-13)

Let F be a p-adic field with residue class field k. We investigate the structure of certain mod p universal modules for GL(3,F) over the corresponding Hecke algebras. To this end, we first study the structure of some mod p universal modules for the finite group GL(n,k) as modules over the corresponding Hecke algebras. We then relate this finite case to the p-adic one by using homological coefficient systems on the the affine Bruhat-Tits building of GL(3). Suppose now that k has cardinality p. We prove that the mod p universal module of GL(3,F) relative to the Iwahori subroup is flat and projective over the Iwahori-Hecke algebra. When replacing the Iwahori subgroup of GL(3,F) by its pro-p-radical, we prove that the corresponding module is flat over the pro-p Iwahori-Hecke algebra if and only if p=2.

1:	Laboratoire de Mathématiques de Versailles (LM-Versailles)
	CNRS : UMR8100 – Université de Versailles Saint-Quentin-en-Yvelines
2:	Columbia University
	Columbia University

Subject

:

Mathematics/Representation Theory

Keyword(s): reductive p-adic group – building – homological coefficient system – universal module

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From: Vincent Sécherre <>

Submitted on: Sunday, 15 May 2011 18:30:33

Updated on: Sunday, 15 May 2011 19:53:51