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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Le foncteur des invariants sous l'action du pro-p-Iwahori de GL2(F)

Rachel Ollivier1

1DMA, ENS, 45 rue d'Ulm, 75230 Paris Cedex 05, France. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2009, Issue 635, Pages 149–185, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2009.078, July 2009

Publication History

Received:
2006-04-03
Revised:
2008-05-01
Published Online:
2009-07-30

Abstract

Let F be a p-adic field with uniformizer π. Given a smooth mod p-representation of G = GL2(F)/π, we consider its subspace of invariants under the action of the pro-p-Iwahori subgroup and get this way a functor taking values in the category of right modules over the pro-p-Hecke algebra with characteristic p. We show that if F = ℚp, this functor restricted to the representations generated by their pro-p-invariants is an equivalence of categories, and give examples of other p-adic fields for which it is not the case.

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