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Number Theory Seminar

Thursday, May 18, 2023
4:00pm to 5:00pm
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Linde Hall 387
Algebraic and arithmetic properties of curves via Galois cohomology
Wanlin Li, Department of Mathematics and Statistics, Washington University in St. Louis,

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 and arithmetic properties of the curve, such as the non-existence of rational points (following Grothendieck's section conjecture) and whether the curve is hyperelliptic.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].