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SUMMARY:Mark Kisin (Harvard)
DTSTART:20211014T190000Z
DTEND:20211014T200000Z
DTSTAMP:20260423T130231Z
UID:MITNT/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/34/">E
 ssential dimension via prismatic cohomology</a>\nby Mark Kisin (Harvard) a
 s part of MIT number theory seminar\n\nLecture held in Room 2-449 in the S
 imons building.\n\nAbstract\nLet $f:Y \\rightarrow X$ be a finite covering
  map of complex algebraic varieties. The essential dimension of $f$ is the
  smallest integer $e$ such that\, birationally\, $f$ arises as the pullbac
 k \nof a covering $Y' \\rightarrow X'$ of dimension $e\,$ via a map $X \\r
 ightarrow X'.$ This invariant goes back to classical questions about reduc
 ing the number of parameters in a solution to a general $n^{\\rm th}$ degr
 ee polynomial\, and appeared in work of Kronecker and Klein on solutions o
 f the quintic. \n\nI will report on joint work with Benson Farb and Jesse 
 Wolfson\, where we introduce a new technique\, 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 $A \\rightarrow A$ has essential dimension $g$ 
 for almost all primes $p.$\n\nNote the unusual time and place: Thursday at
  3pm in 2-449.\n
LOCATION:https://researchseminars.org/talk/MITNT/34/
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