K(π, 1)-neighborhoods and comparison theorems

par Prof. Piotr ACHINGER (Berkeley & IHÉS)

lundi 23 juin 2014, 16:30 → 17:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

A technical ingredient in Faltings' original approach to p-adic comparison theorems involves the construction of K(π, 1)-neighborhoods for a smooth scheme X over a mixed characteristic dvr with a perfect residue field: every point x ∈ X has an open neighborhood U whose general fiber is a K(π, 1) scheme (a notion analogous to having a contractible universal cover). I will show how to extend this result to the logarithmically smooth case, which might help to simplify some proofs in p-adic Hodge theory.