Cohomologie de de Rham du revêtement modéré de la tour de Lubin-Tate

2022/07/03 by Junger, Damien
#11F85 #14F40 #14G35 #20G25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2207.01006

Abstract

In this article, we study the De Rham cohomology of the first cover in the Lubin-Tate tower. In particular, we get a purely local proof that the supercuspidal part realizes the local Jacquet-Langlands correspondence for \rm GL_n by comparing it to the rigid cohomology of some Deligne-Lusztig varieties. The representations obtained are analogous to the ones appearing in the ℓ-adic cohomology if we forget the action of the Weil group. The proof relies on the generalization of an excision result of Grosse-Klönne and on the existence of a semi-stable model constructed by Yoshida for which we give a more explicit description.

Related

• Cohomologie de de Rham du revêtement modéré de l'espace de Drinfeld
• Correspondance locale de Langlands et monodromie des espaces de Drinfeld
• Maximal varieties and the local Langlands correspondence for GL(n)
• On non-abelian Lubin-Tate theory and analytic cohomology
• Comparaison de la cohomologie des tours de Lubin-Tate et de Drinfeld et correspondance de Jacquet-Langlands geometrique