Comparaison de la cohomologie des tours de Lubin-Tate et de Drinfeld et correspondance de Jacquet-Langlands geometrique

Details Comparaison de la cohomologie des tours de Lubin-Tate et de Drinfeld et correspondance de Jacquet-Langlands geometrique Comparaison de la cohomologie des tours de Lubin-Tate et de Drinfeld et correspondance de Jacquet-Langlands geometrique

2006-05-26

arxiv.org/abs/math/0605683v1

Mathematics

Number Theory

72 pages

Scientific paper

This article is the last one about the isomorphism between Lubin-Tate and Drinfeld towers. We prove the existence of an isomorphism between the compactly supported etale cohomology of the Lubin-Tate and Drinfeld towers, and more generally their equivariant cohomology complex. We also prove the existence of a geometric local Jacquet-Langlands correspondence between some equivariant rigid etale sheaves on Gross-Hopkins period space $\mathbb{P}^{n-1}$ and Drinfeld one $\Omega$.

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