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p-adic Geometric Langlands
If you have a question about this talk, please contact Teruyoshi Yoshida.
The (de Rham) geometric Langlands correspondence for GL(n) asserts that to an irreducible rank n integrable connection on a complex smooth projective curve X, we may naturally associate a D-module on Bun_n(X), the moduli stack of rank n vector bundles on X. Making appropriate changes to the formulation there are also Betti and l-adic versions of the above correspondence. In this talk we consider the rigid (and ultimately motivic) side of the story. In particular we conjecture the existence of a p-adic geometric Langlands correspondence relating rank n F-isocrystals on X (now a curve over F_p) to arithmetic D-modules on Bun_n(X). We will also explore the potential of a motivic version of the GLC which should specialize to each of the above correspondences under appropriate realisations. We will assume no specific background in the geometric Langlands correspondence.
This talk is part of the Number Theory Seminar series.
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