MIT Number Theory Seminar

Thursday, October 14, 2021 at 3:00pm to 4:00pm

MIT, 2-143 182 Memorial Drive, Cambridge, MA 02142

Speaker:  Mark Kisin (Harvard University)

Title:  Essential dimension via prismatic cohomology

Abstract:  Let f : YX be a finite covering map of complex algebraic varieties.  The essential dimension of f is the smallest integer eee such that, birationally, f arises as the pullback of a covering Y′X′ of dimension e, via a map XX′.  This invariant goes back to classical questions about reducing the number of parameters in a solution to a general nth degree polynomial, and appeared in work of Kronecker and Klein on solutions of the quintic.

I 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 A has essential dimension g for almost all primes p.


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