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SUMMARY:Cohomology of ($\\phi$\, $\\Gamma$)-modules and duality [MPIM]
DTSTART:20250523T120500Z
DTEND:20250523T140000Z
DTSTAMP:20260416T082600Z
UID:indico-event-419@math-events.uni-bonn.de
DESCRIPTION:Speakers: Yutaro Mikami (University of Tokyo)\n\nOberseminar A
 rithmetic Geometry and Representation Theory\nCohomology of ($\\phi$\, $\\
 Gamma$)-modules was studied by Herr\, Liu\, and Kedlaya-Pottharst-Xiao. Ke
 dlaya-Pottharst-Xiao proved finiteness\, duality\, and Euler-characteristi
 c formula for cohomology of families of ($\\phi$\, $\\Gamma$)-modules.\nIn
  this talk\, we will present an alternative proof of finiteness and dualit
 y by using analytic geometry introduced by Clausen-Scholze and 6-functor f
 ormalism refined by Heyer-Mann. One advantage of this proof is that it can
  handle families over Banach Qp-algebras that are not topologically of fin
 ite type over Qp. If time permits\, we will also discuss potential future 
 applications to the representability of the analytic Emerton-Gee stack.\n
  \n\nhttps://math-events.uni-bonn.de/event/419/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/419/
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