Good reduction of ramified affinoids in the Lubin-Tate perfectoid space
(Université de Tokyo)
Centre de conférences Marilyn et James Simons (IHES)
Centre de conférences Marilyn et James Simons
Le Bois Marie
35, route de Chartres
Recently, Weinstein finds some affinoids in the Lubin-Tate perfectoid space and computes their reduction in equal characteristic case. The cohomology of the reduction realizes the local Langlands correspondence for some representations of GLh, which are unramified in some sense. In this talk, we introduce other affinoids in the Lubin-Tate perfectoid space in equal characteristic case, whose reduction realizes "ramified" representations of conductor exponent h+1. We call them ramified affinoids. We study the cohomology of the reduction and its relation with the local Langlands correspondence. This is a joint work with Takahiro Tsushima.