4 mar 2020 -- 16:30
Aula Magna, DM, Pisa
Seminario di geometria algebrica e aritmetica di Pisa
Abstract.
We use the theory of cohomological invariants for algebraic stacks to completely describe the Brauer group of the moduli stacks Hg of genus g hyperellitic curves over fields of characteristic zero, and the prime-to-char(k) part in positive characteristic. It turns out that the (non-trivial part of the) group is generated by cyclic algebras, by an element coming from a map to the classifying stack of étale algebras of degree 2g+2, and when g is odd by the Brauer-Severi fibration induced by taking the quotient of the universal curve by the hyperelliptic involution. This paints a richer picture than in the case of elliptic curves, where all non-trivial elements come from cyclic algebras. This is joint work with Andrea di Lorenzo.