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SUMMARY:Mod-p Poincaré Duality for some non-proper spaces in p-adic analy
 tic geometry.
DTSTART:20251106T130000Z
DTEND:20251106T150000Z
DTSTAMP:20260505T203500Z
UID:indico-event-15063@indico.math.cnrs.fr
DESCRIPTION:Speakers: Guillaume Pignon-Ywanne\n\np-adic analytic geometry\
 , as started by J.Tate in 1962\, forms a p-adic analogue of complex analyt
 ic geometry\, where spaces are locally defined by convergent power series 
 over extensions of Q_p. Adapting Grothendieck's constructions for schemes\
 , R.Huber constructed a theory of étale cohomology in this setup\, that i
 s very well behaved (admits a six-functor formalism) for l-torsion coeffic
 ients\, with l prime to p. When l = p\, many constructions fail and the si
 tuation is more mysterious\, but results of P.Scholze\, and more recently 
 of L.Mann and B.Zavyalov establish some good properties of cohomology (fin
 iteness of cohomology\, Poincaré duality) for smooth proper spaces\, that
  do not hold in the non-proper setup. These results rely on perfectoid tec
 hniques\, a tool that admits no analogue in algebraic geometry. \nIn this
  talk\, after recollecting the necessary background on p-adic geometry and
  étale cohomology\, I will present the key ideas behind the results above
 \, before focusing on some of my work on extending Poincaré Duality to so
 me non-proper spaces admitting a nicely controlled geometry\, such as Drin
 feld's symmetric spaces. No prior knowledge of p-adic analytic geometry is
  required ! \n \n\nhttps://indico.math.cnrs.fr/event/15063/
LOCATION:M7-411
URL:https://indico.math.cnrs.fr/event/15063/
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