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SUMMARY:A p-adic Riemann-Hilbert functor
DTSTART:20260512T123000Z
DTEND:20260512T140000Z
DTSTAMP:20260523T230800Z
UID:indico-event-16571@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr\;jasserand@ihes.fr
DESCRIPTION:Speakers: Vadim Vologodsky (University of Chicago & IHES)\n\nT
 he parallel transport construction can be used to produce an equivalence o
 f categories between the category of representations of the fundamental gr
 oup of a smooth connected manifold and the category of flat bundles over t
 his manifold. I will discuss an analogue of this construction when the fie
 ld of real numbers is replaced by the field of p-adic numbers. Given a smo
 oth rigid space X over ℚp\, consider the ring D of differential operator
 s on the base change of X to Fontaine's period ring BdR+. Let Dt be the su
 balgebra spanned by functions and vector fields multiplied by a uniformize
 r t in BdR+. Thus\, Dt is an algebra over BdR+\, whose mod t reduction is 
 the commutative algebra of functions on the cotangent space\, and which is
  isomorphic to D after inverting t. The category of modules over Dt can be
  twisted by any μp∞ gerbe over the cotangent space. I will construct a 
 functor from the category of étale BdR+-local systems on XCp to the categ
 ory of modules over Dt twisted by the Simpson gerbe. The composition of th
 is functor with the mod t reduction recovers the p-adic Simpson functor of
  Bhatt and Zhang.\n \nThis is a joint work in progress with Bhargav Bhatt
 \, Ben Heuer and Alexander Petrov.\n \n========\nPour être informé des 
 prochains séminaires vous pouvez vous abonner à la liste de diffusion en
  écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscri
 be seminaire_mathematique PRENOM NOM"(indiquez vos propres prénom et nom)
  et laissez le corps du message vide.\n\nhttps://indico.math.cnrs.fr/event
 /16571/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/16571/
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