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SUMMARY:Guido Bosco (IMJ)
DTSTART:20210617T160000Z
DTEND:20210617T172000Z
DTSTAMP:20260423T021300Z
UID:RAMpAGe/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/40/"
 >Rational p-adic Hodge theory for non-proper rigid-analytic varieties</a>\
 nby Guido Bosco (IMJ) as part of Recent Advances in Modern p-Adic Geometry
  (RAMpAGe)\n\n\nAbstract\nThe goal of this talk will be to discuss the rat
 ional p-adic Hodge\ntheory of general smooth rigid-analytic varieties. The
  study of this\nsubject for varieties that are not necessarily proper (e.g
 . Stein) is\nmotivated in part by the desire of finding a geometric incarn
 ation of\nthe p-adic Langlands correspondence in the cohomology of local S
 himura\nvarieties. In this context\, one difficulty is that the relevant\n
 cohomology groups (such as the p-adic (pro-)étale\, and de Rham ones) are
 \nusually infinite-dimensional\, and\, to study them\, it becomes importan
 t\nto exploit the topological structure that they carry. But\, in doing so
 \,\none quickly runs into several topological issues: for example\, the de
 \nRham cohomology groups of a smooth affinoid space are\, in general\, not
 \nHausdorff. We will explain how to overcome these issues\, using the\ncon
 densed and solid formalisms recently developed by Clausen and\nScholze\, a
 nd we will report on a comparison theorem describing the\ngeometric p-adic
  (pro-)étale cohomology in terms of de Rham data\, for a\nlarge class of 
 smooth rigid-analytic varieties defined over a p-adic\nfield. In particula
 r\, we recover results of Colmez\, Dospinescu\, and\nNizioł.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/40/
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