Wild ramification and spaces

• 成果类型: Article
• 署名作者: Achinger, Piotr
• 署名单位: Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Universite Paris Saclay
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0733-5
• 发表日期: 2017
• 页码: 453-499
• 关键词: etale; coverings; k(pi

摘要

We prove that every connected affine scheme of positive characteristic is a space for the ,tale topology. The main ingredient is the special case of the affine space over a field k. This is dealt with by induction on n, using a key Bertini-type statement regarding the wild ramification of -adic local systems on affine spaces, which might be of independent interest. Its proof uses in an essential way recent advances in higher ramification theory due to T. Saito. We also give rigid analytic and mixed characteristic versions of the main result.