Evaluating the wild Brauer group

Inventiones mathematicae, vol. 234, pp. 819–891

Abstract

Abstract Classifying elements of the Brauer group of a variety $X$ X over a $p$ p -adic field by the $p$ p -adic accuracy needed to evaluate them gives a filtration on $\operatorname{Br}X$ Br X . We relate this filtration to that defined by Kato’s Swan conductor. The refined Swan conductor controls how the evaluation maps vary on $p$ p -adic discs: this provides a geometric characterisation of the refined Swan conductor. We give applications to rational points on varieties over number fields, including failure of weak approximation for varieties admitting a non-zero global 2-form.

Authors 1

1. Rachel Newton corresponding

   King's College London

   Affiliation as printed

   Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, UK

   Department of Mathematics, King’s College London, London, UK