AVVISO SEMINARI DI MATEMATICA

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Data: mercoledì 4 MARZO 2020

Luogo: Aula Magna del Dipartimento di Matematica di Pisa

Programma:

15:00--16:00 Mattia Talpo (Università di Pisa): Topological realization over C((t)) via Kato-Nakayama spaces

Abstract: I will report on some joint work with Piotr Achinger, about a “Betti realization” functor for varieties over the formal punctured disk Spec C((t)), i.e. defined by polynomials with coefficients in the field of formal Laurent series in one variable over the complex numbers. We give two constructions producing the same result, and one of them is via “good models” over the power series ring C[[t]] and the “Kato-Nakayama” construction in logarithmic geometry, that I will review during the talk.

16:00--16:30 Coffee break

16:30--17:30  Roberto Pirisi (Stockholm): Brauer groups of moduli of hyperelliptic curves, via cohomological invariants

Abstract: We use the theory of cohomological invariants for algebraic stacks to completely describe the Brauer group of the moduli stacks H_g 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.