Department Colloquium

Fri., Oct. 7, 2022 3:30 p.m.

Location: Live Stream

Speaker: Inna Zakharevich, Cornell University

Title: Point counting with twists (495 kB)

Zoom Link: https://uregina-ca.zoom.us/j/92508741353?pwd=UzFOMjVMelVkRWhqR215cjd6dTlCQT09

Abstract:

Consider a variety over a finite field. The number of points over the field is not only an invariant of the variety, but also of its "scissors congruence" type: of we cut up the variety into locally closed pieces, and rearrange those pieces into another variety, the number of points does not change. Moreover, if we have an automorphism of a variety, the permutation induced on the points is similarly an invariant of the automorphism. In this talk we will discuss a way of enhancing this invariant to an invariant which can distinguish different types of automorphisms and use it to detect some interesting structures in the higher K-theory groups of varieties.