Frobenius gauges and a new theory of p-torsion sheaves in characteristic p. I

2013/04/12 by Jean-Marc Fontaine, Fontaine, Jean-Marc, Uwe Jannsen +1 · 1 citation
Mathematics · #14F20 #14F30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1304.3740

openalex publication_date 2013/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a new cohomology theory in characteristic p>0, the so called F-gauge cohomology, a cohomology with values in the category of so-called F-gauges, which refines the cristalline cohomology. In this first paper we mainly discuss the theory for smooth projective varieties over perfect fields of charatceristic p. We also compare our theory with other existing structures like the F-zips of Moonen and Wedhorn and the displays of Langer and Zink.

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