Speaker
Description
In joint work with Andrea di Lorenzo we computed the Brauer groups of
the moduli stacks of genus three curves and abelian varieties of
dimension three. A crucial step involved constructing explicit classes
by leveraging odd theta characteristics and the map they induced to the
moduli stack of étale algebras of degree 28. Three problems remained
open: computing the pullback map from the Brauer group of the moduli
stack of genus three curves to that of hyperelliptic genus three curves,
computing the full cohomological invariants of the moduli stack of genus
three curves, and whether theta characteristics induce higher nontrivial
cohomology classes for higher genus.
In this talk I will describe recent joint work with Andrés Jaramillo
Puentes where we answer the first and third question, showing that the
pullback between Brauer groups is injective and producing new mod 2
cohomology classes (of degree 2^(g-1)) on the moduli stacks of genus g
curves and dimension g abelian varieties over a totally real field.
These classes are, borrowing a term from Serre’s study of group
cohomology, non-negligible, and in particular cannot come from the cycle
map.
