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SUMMARY:p-adic Geometric Langlands - Alexander Paulin (King's College Lond
 on)
DTSTART:20121127T143000Z
DTEND:20121127T153000Z
UID:TALK40563@talks.cam.ac.uk
CONTACT:Teruyoshi Yoshida
DESCRIPTION:The (de Rham) geometric Langlands correspondence for GL(n) ass
 erts\nthat to an irreducible rank n integrable connection on a complex\nsm
 ooth projective curve X\, we may naturally associate a D-module\non Bun_n(
 X)\, the moduli stack of rank n vector bundles on X.\nMaking appropriate c
 hanges to the formulation there are also Betti and\nl-adic versions of the
  above correspondence.  In this talk we\nconsider the rigid (and ultimatel
 y motivic) side of the story. In\nparticular we conjecture the existence o
 f a p-adic geometric\nLanglands correspondence relating rank n F-isocrysta
 ls on X (now\na curve over F_p) to arithmetic D-modules on Bun_n(X).  We w
 ill\nalso explore the potential of a motivic version of the GLC which\nsho
 uld specialize to each of the above correspondences under\nappropriate rea
 lisations.  We will assume no specific background in\nthe geometric Langla
 nds correspondence.
LOCATION:MR13
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