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SUMMARY:Mark Kisin (Harvard University)
DTSTART:20211111T180000Z
DTEND:20211111T192000Z
DTSTAMP:20260423T021403Z
UID:RAMpAGe/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/58/"
 >Essential dimension via prismatic cohomology</a>\nby Mark Kisin (Harvard 
 University) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)
 \n\n\nAbstract\nLet $f\\colon Y→X$ be a finite covering map of complex a
 lgebraic varieties. The essential dimension of f is the smallest integer e
  such that\, birationally\, $f$ arises as the pullback of a covering $Y′
 →X′$ of dimension $e$\, via a map $X→X′$. This invariant goes back
  to classical questions about reducing the number of parameters in a solut
 ion to a general nth degree polynomial\, and appeared in work of Kronecker
  and Klein on solutions of the quintic. \n\nI will report on joint work wi
 th Benson Farb and Jesse Wolfson\, where we introduce a new technique\, us
 ing prismatic cohomology\, to obtain lower bounds on the essential dimensi
 on of certain coverings. For example\, we show that for an abelian variety
  $A$ of dimension $g$ the multiplication by $p$ map $A→A$ has essential 
 dimension $g$ for almost all primes $p$.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/58/
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