Séminaire d'arithmétique à Lyon

Wild ramification and K(pi, 1) spaces

par Piotr Achinger (IHES)

Europe/Paris
Salle A1 (UMPA, ENS de Lyon)

Salle A1

UMPA, ENS de Lyon

Description
I will sketch the proof 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. Time permitting, I will discuss some "anabelian" and "irregular" ramifications of the result.