Wild ramification and K(pi, 1) spaces
Algebraic Geometry
2017-11-22 v2
Abstract
We prove that every connected affine scheme of positive characteristic is a K(pi, 1) space for the etale 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 l-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.
Keywords
Cite
@article{arxiv.1701.03197,
title = {Wild ramification and K(pi, 1) spaces},
author = {Piotr Achinger},
journal= {arXiv preprint arXiv:1701.03197},
year = {2017}
}
Comments
32 pages, 1 figure; Corrected a mistake in the proof of Theorem 1.3.1 found by an anonymous referee. Numerous minor changes. To appear in Inventiones Mathematicae