Wild Brauer classes via prismatic cohomology

Margherita Pagano (Imperial College London)

Wednesday 22nd October 16:00-17:00
Maths 311B

Abstract

Let K be a finite extension of the field of p-adic numbers and X a smooth proper K-variety with good reduction. I will show how, under a mild assumption on the behaviour of Hodge numbers under reduction modulo p, the existence of a non-zero global 2-form on the special fibre (hence, in positive characteristic p) implies the existence of p-torsion Brauer classes with interesting arithmetic properties on the generic fibre (hence, in characteristic 0). If times permit, I will then explain how this implies that any smooth proper variety over a number field which satisfies weak approximation over all finite extensions has no non-zero global 2-form.

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