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Documents  11S37 | enregistrements trouvés : 2

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Spherical Hecke algebra, Satake transform, and an introduction to local Langlands correspondence.

20C08 ; 22E50 ; 11S37

We report on progress towards a theory of local Shimura varieties for $p$-adic fields, in parallel with the theory of local shtukas for $\mathbb{F}_q((t))$. 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. We report on progress towards a theory of local Shimura varieties for $p$-adic fields, in parallel with the theory of local shtukas for $\mathbb{F}_q((t))$. 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 ...

14G35 ; 11S37

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