Deligne--Illusie Classes as Arithmetic Kodaira--Spencer Classes

Taylor Dupuy; David Zureick-Brown

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arXiv · 1804.00228

Deligne--Illusie Classes as Arithmetic Kodaira--Spencer Classes

Taylor Dupuy·David Zureick-Brown

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Abstract

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. Afterwards we discuss a "wittfinitesimal Torelli problem" and its relation to CM Jacobians.

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Taylor Dupuy, David Zureick-Brown. 2018-03-31. Deligne--Illusie Classes as Arithmetic Kodaira--Spencer Classes. https://arxiv.org/abs/1804.00228

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