# Duality in the cohomology of crystalline local systems

Research paper by WIESŁAWA NIZIOL

Indexed on: 01 Oct '97Published on: 01 Oct '97Published in: Compositio Mathematica

#### Abstract

Let k be a perfect field of a positive characteristic p, K-the fraction field of the ring of Witt vectors W(k) Let X be a smooth and proper scheme over W(k). We present a candidate for a cohomology theory with coefficients in crystalline local systems: p -adic étale local systems on X_K characterized by associating to them so called Fontaine-crystals on the crystalline site of the special fiber Xk. We show that this cohomology satysfies a duality theorem.