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 ».
Accepted:
Published online:
Classification: 12H05, 11G99
Keywords: -derivations, Frobenius lifts, semi-linear
Author's affiliations:
@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/} }
TY - JOUR TI - Deligne–Illusie Classes as Arithmetic Kodaira–Spencer Classes JO - Journal de Théorie des Nombres de Bordeaux PY - 2019 DA - 2019/// SP - 371 EP - 383 VL - 31 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1086/ UR - https://doi.org/10.5802/jtnb.1086 DO - 10.5802/jtnb.1086 LA - en ID - JTNB_2019__31_2_371_0 ER -
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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