Algebraic/Arithmetic properties of curves and Galois cohomology 

Job Candidate Talk
Wednesday, February 2, 2022 - 11:00am for 1 hour (actually 50 minutes)
Wanlin Li – CRM Montreal –
Anton Leykin

A lot of the algebraic and arithmetic information of a curve is contained in its interaction with the Galois group. This draws inspiration from topology, where given a family of curves over a base B, the fundamental group of B acts on the cohomology of the fiber. As an arithmetic analogue, given an algebraic curve C defined over a non-algebraically closed field K, the absolute Galois group of K acts on the etale cohomology of the geometric fiber and this action gives rise to various Galois cohomology classes. In this talk, we discuss how to use these classes to detect algebraic/arithmetic properties of the curve, such as the rational points (following Grothendieck's section conjecture), whether the curve is hyperelliptic, and the set of ``supersingular'' primes.