R202, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 202室)

Affinoids in the Lubin-Tate Space at Infinite Level and the Local Langlands Correspondence

Kazuki Tokimoto (Academia Sinica)

Abstract:

The l-adic etale cohomology of the Lubin-Tate spaces is known to realize the local Langlands correspondence for GL(n) and the local Jacquet-Langlands correspondence (the non-abelian Lubin-Tate theory). While it is highly interesting and important, the known proof is somewhat indirect and does not tell much about the relation between representations and the geometry of the Lubin-Tate spaces.

In this talk I will explain a result where families of affinoid subspaces of the limit space of the Lubin-Tate spaces are constructed and the l-adic cohomology of each reduction realizes the correspondences for a certain class of representations.

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