Title: Brauer groups of schemes associated to symmetric powers of smooth projective curves in arbitrary characteristics
Speaker: Roy Joshua
Abstract: The theory of Brauer groups has a long and rich history. In recent years there seems to be a renewed interest in this area, and there have been several important developments in the last 10-15 years using sophisticated techniques. It is also one of the few topics that can be studied both from a complex algebraic geometry point of view as well as using algebraic tools, notably ́etale cohomology. In this talk we show that the \ell^n -torsion part of the cohomological Brauer groups of certain schemes associated to symmetric powers of a projective smooth curve over a separably closed field k are isomorphic, when \ell is invertible in k. The schemes considered are the symmetric powers themselves, then the corresponding Picard schemes and also certain Quot-schemes. We also obtain similar results for Prym varieties associated to certain finite covers of such curves. This is joint work with Jaya Iyer.
Note: This is a new seminar run jointly by Jennifer Park, Eric Katz and Roy Joshua. We plan to run it more or less every other Tuesday at 4:15. The seminar website is: https://people.math.osu.edu/joshua.1/ArithGeomSeminar
