Deligne--Illusie Classes as Arithmetic Kodaira--Spencer Classes
Taylor Dupuy, David Zureick-Brown

TL;DR
This paper demonstrates that Deligne--Illusie classes fulfill a modified version of Faltings' non-existent arithmetic Kodaira--Spencer classes, and explores related Torelli problems and CM Jacobians.
Contribution
It introduces a modified compatibility condition showing Deligne--Illusie classes satisfy an arithmetic Kodaira--Spencer type property, extending prior non-existence results.
Findings
Deligne--Illusie classes meet a modified compatibility condition
Discussion of Wittfinitesimal Torelli problem and CM Jacobians
Extension of Faltings' non-existence results to new classes
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Commutative Algebra and Its Applications
