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Relative Algebraic Differential Characters

Spencer Bloch·Hélène Esnault
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Abstract

Let $f: X \to S$ be a smooth morphism in characteristic 0, and let $(E, \nabla_{X/S})$ be a relative regular connection. We define a cohomology of relative differential characters on $X$ which receives classes of $(E, \nabla_{X/S})$. It says in particular that the partial vanishing of the trace of the iterated Atiyah classs can be made canonical. While applied to a family of curves and $c_2$, the construction yields a connection of $f_*c_2(E)$. This one has been constructed analytically by A. Beilinson. We also relate our construction to the trace complex of Beilinson of Schechtman.

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Spencer Bloch, Hélène Esnault. 1999-12-02. Relative Algebraic Differential Characters. https://arxiv.org/abs/math/9912015

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