A $p$-adic local invariant cycle theorem with applications to Brauer groups

Yanshuai Qin

paper

A $p$ -adic local invariant cycle theorem with applications to Brauer groups

arXiv:2103.04945

Abstract

In this article, we prove a $p$ -adic analogue of the local invariant cycle theorem for $H^{2}$ in mixed characteristics. As a result, for a smooth projective variety $X$ over a $p$ -adic local field $K$ with a proper flat regular model $X$ over $O_{K}$ , we show that the natural map $B r (X) \to B r (X_{K ˉ})^{G_{K}}$ has a finite kernel and a finite cokernel. And we prove that the natural map $H o m (B r (X) / B r (K) + B r (X), Q / Z) \to A l b_{X} (K)$ has a finite kernel and a finite cokernel, generalizing Lichtenbaum's duality between Brauer groups and Jacobians for curves to arbitrary dimensions.

This preprint has been incorporated into arXiv:2103.06910

A p-adic local invariant cycle theorem with applications to Brauer groups

Abstract

References in corpus (2)

A $p$ -adic local invariant cycle theorem with applications to Brauer groups