Deligne–Illusie Classes as Arithmetic Kodaira–Spencer Classes
Taylor Dupuy ; David Zureick-Brown
Journal de Théorie des Nombres de Bordeaux, Tome 31 (2019) no. 2, pp. 371-383.

Faltings a montré qu’il n’y a pas de « classes de Kodaira–Spencer arithmétiques » satisfaisant à un certain axiome de compatibilité. En modifiant légèrement ses définitions, nous montrons que les classes de Deligne–Illusie satisfont à ce que l’on pourrait considérer comme « condition de compatibilité de Kodaira–Spencer arithmétique ».

Faltings showed that “arithmetic Kodaira–Spencer classes” satisfying a certain compatibility axiom cannot exist. By modifying his definitions slightly, we show that the Deligne–Illusie classes satisfy what could be considered an “arithmetic Kodaira–Spencer” compatibility condition.

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DOI : https://doi.org/10.5802/jtnb.1086
Classification : 12H05,  11G99
Mots clés : p-derivations, Frobenius lifts, semi-linear 
@article{JTNB_2019__31_2_371_0,
     author = {Taylor Dupuy and David Zureick-Brown},
     title = {Deligne{\textendash}Illusie {Classes} as {Arithmetic} {Kodaira{\textendash}Spencer} {Classes}},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {371--383},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {2},
     year = {2019},
     doi = {10.5802/jtnb.1086},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1086/}
}
Taylor Dupuy; David Zureick-Brown. Deligne–Illusie Classes as Arithmetic Kodaira–Spencer Classes. Journal de Théorie des Nombres de Bordeaux, Tome 31 (2019) no. 2, pp. 371-383. doi : 10.5802/jtnb.1086. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1086/

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