Jared Weinstein: Local Shimura varieties for p-adic fields
Автор: Centre International de Rencontres Mathématiques
Загружено: 2015-06-08
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We report on progress towards a theory of local Shimura varieties for p-adic fields, in parallel with the theory of local shtukas for Fq((t)). Using perfectoid spaces (in particular Scholze's theory of "diamonds"), it is possible to give a unified definition of local shtukas which incorporates both the equal and unequal characteristic cases. Conjecturally, if G is a reductive group, the cohomology of a moduli space of local G-shtukas should realize the Langlands correspondence for G in a systematic way (along the lines described by V. Lafforgue for global stukas). This talk will draw heavily from ideas of Peter Scholze and Laurent Fargues.
Recording during the thematic meeting: "Arithmetics of Shimura varieties, of automorphic forms and applications" the July 01, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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