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arXiv · 2009.03282

Evaluating the wild Brauer group

Martin Bright·Rachel Newton
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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.

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Martin Bright, Rachel Newton. 2020-09-07. Evaluating the wild Brauer group. https://doi.org/10.1007/s00222-023-01210-8

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