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 X k. We show that this cohomology satysfies a duality theorem.
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NIZIOL, W. Duality in the cohomology of crystalline local systems. Compositio Mathematica 109, 67–97 (1997). https://doi.org/10.1023/A:1000100917913
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DOI: https://doi.org/10.1023/A:1000100917913