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SUMMARY:Mark Kisin (Harvard University)
DTSTART:20211012T140000Z
DTEND:20211012T160000Z
DTSTAMP:20260422T102246Z
UID:FGC-IPM/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGC-IPM/2/">
 Essential dimension via prismatic cohomology</a>\nby Mark Kisin (Harvard U
 niversity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nLe
 t $f:Y \\rightarrow X$ be a finite covering map of complex algebraic varie
 ties. The essential dimension of $f$ is the smallest integer $e$ such that
 \, birationally\, $f$ arises as the pullback of a covering $Y'\\rightarrow
  X'$ of dimension $e$\, via a map $X \\rightarrow X'$. This invariant goes
  back to classical questions about reducing the number of parameters in a 
 solution to a general $n$-th degree polynomial\, and appeared in work of K
 ronecker and Klein on solutions of the quintic. \n\nI will report on joint
  work with Benson Farb and Jesse Wolfson\, where we introduce a new techni
 que\, using prismatic cohomology\, to obtain lower bounds on the essential
  dimension of certain coverings. For example\, we show that for an abelian
  variety $A$ of dimension $g$ the multiplication by $p$ map $A  \\rightarr
 ow A$ has essential dimension $g$ for almost all primes $p$.\n\nMeeting ID
 : 908 611 6889 \,\nPasscode: order of the symmetric group on 9 letters (ty
 pe the 6-digit number)\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/2/
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