Séance Séminaire

Séminaire de Théorie des Nombres de Montpellier

« Stable reduction of Lubin-Tate spaces »

Let F be a local field and $\ldots\rightarrow X(\pi^2)\rightarrow X(\pi)\rightarrow X(1)$ the Lubin-Tate tower of dimension one corresponding to F. By a result of Carayol (generalized by Harris and Taylor to arbitrary dimension), the étale cohomology of this tower realizes the local Langlands and the Jacquet-Langlands correspondence for $\mathrm{GL}_2(F)$. In this talk I will report on recent results concerning the stable reduction of $X(\pi^n)$ for all n. Using these results one can give a purely local proof of Carayol's theorem, at least for residue characteristic 2.