论文标题
评估野生brauer组
Evaluating the wild Brauer group
论文作者
论文摘要
根据评估它们所需的P-ADIC准确性在P-ADIC领域上的Brauer组的元素分类。我们将这种过滤与Kato Swan指挥所定义的过滤相关联。精致的天鹅指挥控制了评估图在P-ADIC碟片上的变化：这提供了精制天鹅导体的几何表征。我们将在数字字段上的品种上的合理点提供了应用，包括承认非零全球2形式的品种弱近似失败。
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.
