Geodesic
Frobenius gauges and a new theory of $p$-torsion sheaves in characteristic $p$
Documenta mathematica, Tome 26 (2021), pp. 65-101 Cet article a éte moissonné depuis la source EMS Press

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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 B. Moonen and T. Wedhorn [Int. Math. Res. Not. 2004, No. 72, 3855–3903 (2004; Zbl 1084.14023)] and the displays of A. Langer and T. Zink [Doc. Math. 12, 147–191 (2007; Zbl 1122.14016)].
DOI : 10.4171/dm/809
Classification : 14F20, 14F30
Mots-clés : crystalline cohomology, gauges, p-torsion sheaves, gauge cohomology, Dieudonne modules 
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     author = {Jean-Marc Fontaine and Uwe Jannsen},
     title = {Frobenius gauges and a new theory of $p$-torsion sheaves in characteristic $p$},
     journal = {Documenta mathematica},
     pages = {65--101},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/809},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/809/}
}
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Jean-Marc Fontaine; Uwe Jannsen. Frobenius gauges and a new theory of $p$-torsion sheaves in characteristic $p$. Documenta mathematica, Tome 26 (2021), pp. 65-101. doi: 10.4171/dm/809

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