Lefschetz trace formula and l-adic cohomology of Lubin-Tate tower

Réseaux d'induction des représentations elliptiques de Lubin-Tate

We study the reduction modulo $l$ of some elliptic representations; for each of these representations, we give a particular lattice naturally obtained by parabolic induction in giving the graph of extensions between its irreducible sub-quotient of its reduction modulo $l$. The principal motivation for this work, is that these lattices appear in the cohomology of Lubin-Tate towers.

Multivariable Lubin-Tate (ϕ,Γ)-modules and filtered ϕ-modules

We define some rings of power series in several variables, that are attached to a Lubin-Tate formal module. We then give some examples of (ϕ,Γ)-modules over those rings. They are the global sections of some reflexive sheaves on the p-adic open unit polydisk, that are constructed from a filtered ϕ-module using a modification process. We prove that we obtain every crystalline (ϕ,Γ)-module over those rings in this way.

卢宾-泰特和德拉姆束的范畴

The Categories of Lubin-Tate and Drinfeld Bundles

研究有限扩张F上的n维德拉姆对称空间上卢宾-泰特束的范畴等价于F上不变量为1/n的除法代数单位群的有限维光滑表示范畴

On the p-adic cohomology of the Lubin-Tate tower

We prove a finiteness result for the p-adic cohomology of the Lubin-Tate tower. For any n>=1 and p-adic field F, this provides a canonical functor from admissible p-adic representations of GL_n(F) towards admissible p-adic representations of Gal_F x D^*, where Gal_F is the absolute Galois group of F, and D/F is the central division algebra of invariant 1/n. Moreover, we verify a local-global-compatibility statement for this correspondence, and compatibility with the patching construction of Caraiani-Emerton-Gee-Geraghty-Paskunas-Shin.

Théorie de Lubin-Tate non abélienne l-entière

For two distinct primes p and l, we investigate the Z_l-cohomology of the Lubin-Tate towers of a p-adic field. We prove that it realizes some version of Langlands and Jacquet-Langlands correspondences for flat families of irreducible supercuspidal representations parametrized by a Z_l-algebra R, in a way compatible with extension of scalars. When R is a field of characteristic l, this gives a cohomological realization of the Langlands-Vigneras correspondence for supercuspidals, and a new proof of its existence. When R runs over complete local algebras, this provides bijections between deformat…

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

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 $\ell$-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…