NT Seminar Tomorrow: Niven Achenjang (MIT) 11am PDL C401

[Bianca Viray]

Hi everyone,

Our seminar speaker tomorrow is Niven Achenjang from MIT and he will be speaking on The Brauer Group of Stacky Y_0(2). As usual, we will go to lunch with the speaker after the talk.

Abstract: The Brauer groups Br(-) = H^2(-, Gm) of fields and schemes have found much utility in number theory, but Brauer groups of stacks have yet to receive as much attention. In this setting, new phenomena emerge; for example, the Brauer group of a stacky curve over an algebraically closed field can still be non-trivial, i.e. the analogue of Tsen's theorem fails. In this talk, after summarizing some of the previous work on the Gm-cohomology of modular curves, I will explain how one can compute the Brauer group of Y_0(2), the modular curve parameterizing elliptic curves equipped with a cyclic subgroup of order 2. Along the way, I hope to indicate which features of this computation one should expect to generalize to other modular curves as well as to indicate which features I personally am not yet sure how to fit into a nice general picture. This is joint work with Deewang Bhamidipati, Aashraya Jha, Caleb Ji, and Rose Lopez.

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Bianca Viray (she/her)

Craig McKibben and Sarah Merner Professor of Mathematics

University of Washington

Seattle, WA 98195

https://sites.math.washington.edu/~bviray/