Evaluating the wild Brauer group
Algebraic Geometry
2023-10-06 v5 Number Theory
Abstract
Classifying elements of the Brauer group of a variety X over a p-adic field according to the p-adic accuracy needed to evaluate them gives a filtration on 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-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.
Keywords
Cite
@article{arxiv.2009.03282,
title = {Evaluating the wild Brauer group},
author = {Martin Bright and Rachel Newton},
journal= {arXiv preprint arXiv:2009.03282},
year = {2023}
}
Comments
58 pages; minor changes. Final version. The Version of Record of this article is published in Inventiones Mathematicae and is available online at https://doi.org/10.1007/s00222-023-01210-8