Evaluating the wild Brauer group

• 成果类型: Article
• 署名作者: Bright, Martin; Newton, Rachel
• 署名单位: University of London; King's College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01210-8
• 发表日期: 2023
• 页码: 819-891
• 关键词: weak approximation; conductors; VARIETIES; reduction; torsion; FIELDS; etale

摘要

Classifying elements of the Brauer group of a variety X over a p-adic field by 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 con-trols how the evaluation maps vary on p-adic discs: this provides a geometric char-acterisation 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.