Piotr Achinger "Wild ramification and K(pi,1) spaces"

Piotr Achinger (IHES)
Wild ramification and K(pi,1) spaces

We will prove that every connected affine scheme in positive characteristic is a K(pi,1) space for the etale topology. The key technical ingredient is a “Bertini-type” statement regarding the wild ramification of l-adic local systems on affine spaces. Its proof uses in an essential way recent advances in higher ramification theory due to T. Saito.