Geodesic
Frobenius gauges and a new theory of $p$-torsion sheaves in characteristic $p$
Documenta mathematica, Tome 26 (2021), pp. 65-101.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 crystalline cohomology. We mainly discuss the theory for smooth projective varieties over perfect fields of characteristic $p$. We also compare our theory with other existing structures like the $F$-zips of \textit{B. Moonen} and \textit{T. Wedhorn} [Int. Math. Res. Not. 2004, No. 72, 3855--3903 (2004; Zbl 1084.14023)] and the displays of \textit{A. Langer} and \textit{T. Zink} [Doc. Math. 12, 147--191 (2007; Zbl 1122.14016)].
Classification : 14F20, 14F30
Keywords: gauges, \(p\)-torsion sheaves, gauge cohomology, crystalline cohomology, Dieudonne modules 
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     author = {Fontaine, Jean-Marc and Jannsen, Uwe},
     title = {Frobenius gauges and a new theory of \(p\)-torsion sheaves in characteristic \(p\)},
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     year = {2021},
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Fontaine, Jean-Marc; Jannsen, Uwe. Frobenius gauges and a new theory of \(p\)-torsion sheaves in characteristic \(p\). Documenta mathematica, Tome 26 (2021), pp. 65-101. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a55/