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SUMMARY:Lucas Mann (Bonn)
DTSTART:20210218T170000Z
DTEND:20210218T182000Z
DTSTAMP:20260423T035746Z
UID:RAMpAGe/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/37/"
 >$p$-adic six functors on diamonds</a>\nby Lucas Mann (Bonn) as part of Re
 cent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nMotivated
  by $p$-adic Poincaré duality in rigid geometry\, we develop a $p$-adic s
 ix functor formalism on rigid varieties\, or more generally for diamonds. 
 This is achieved by defining a category of "quasi-coherent $\\mathcal{O}_X
 ^+/p$-modules" on a diamond $X$ and then using the recent development of a
  quasi-coherent 6-functor formalism on schemes by Clausen-Scholze to obtai
 n a similar 6-functor formalism on diamonds. One easily deduces the desire
 d p-adic Poincaré duality on a smooth proper rigid variety $X$ in mixed c
 haracteristic\, noting that by Scholze's primitive comparison theorem\, $\
 \mathbb F_p$-cohomology on $X$ can be computed via cohomology of the sheaf
  $O_X^+/p$. Of course\, our p-adic 6-functor formalism allows for many mor
 e potential applications\; for example\, we expect to gain new insights in
  the $p$-adic Langlands program.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/37/
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