Deligne–Illusie Classes as Arithmetic Kodaira–Spencer Classes
Taylor Dupuy1; David Zureick-Brown2
1 Department of Mathematics & Statistics University of Vermont, USA
2 Dept. of Math and CS Emory University 400 Dowman Dr., W401 Atlanta, GA 30322, USA
Journal de théorie des nombres de Bordeaux, Volume 31 (2019) no. 2, pp. 371-383.

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.

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 ».

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.1086
Classification: 12H05, 11G99
Keywords: $p$-derivations, Frobenius lifts, semi-linear

Taylor Dupuy 1; David Zureick-Brown 2

1 Department of Mathematics & Statistics University of Vermont, USA
2 Dept. of Math and CS Emory University 400 Dowman Dr., W401 Atlanta, GA 30322, USA
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Taylor Dupuy; David Zureick-Brown. Deligne–Illusie Classes as Arithmetic Kodaira–Spencer Classes. Journal de théorie des nombres de Bordeaux, Volume 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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