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Pré-Publication, Document De Travail Année : 2016

Equivalences of tame blocks for p-adic linear groups

Résumé

Let p and ℓ be two distinct primes, F a p-adic field and n an integer. We show that any level 0 block of the category of smooth Z ℓ-valued representations of GL n (F) is equivalent to the unipotent block of an appropriate product of GL n i (F i). To this end, we first show that the level 0 category of GL n (F) is equivalent to a category of " modules " over a certain Z ℓ-algebra " with many objects " whose definition only involves n and the residue field of F. Then we use fine properties of Deligne-Lusztig cohomology to split this algebra and produce suitable Morita equivalences.
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Dates et versions

hal-01292714 , version 1 (23-03-2016)

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Jean-François Dat. Equivalences of tame blocks for p-adic linear groups. 2016. ⟨hal-01292714⟩
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