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SUMMARY:Hiroki Kato (Paris Saclay)
DTSTART:20210311T170000Z
DTEND:20210311T182000Z
DTSTAMP:20260423T021303Z
UID:RAMpAGe/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/38/"
 >Etale cohomology of algebraizable rigid analytic varieties via nearby cyc
 les over general bases</a>\nby Hiroki Kato (Paris Saclay) as part of Recen
 t Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nOne of the m
 ost fundamental results in the study of étale cohomology of rigid analyti
 c varieties is the comparison with the nearby cycle cohomology\, which giv
 es a canonical isomorphism between the cohomology of an algebraizable rigi
 d analytic variety and the cohomology of the nearby cycle. \nI will discus
 s a generalization of this comparison result to the relative case: For an 
 algebraizable morphism\, the compactly supported higher direct image sheav
 es are identified\, up to replacing the target by a blowup\, with a genera
 lization of the nearby cycle cohomology\, which is given by the theory of 
 nearby cycles over general bases. \nThis result can be used to show the ex
 istence of a tubular neighborhood that doesn’t change the cohomology for
  algebraizable families.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/38/
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