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Relative Algebraic Differential Characters

1999/12/02 by Spencer Bloch, Bloch, Spencer, Hélène Esnault +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.math/9912015

Latex 2e, 25 pages

arxiv created 1999/12/02 · openalex publication_date 1999/12/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f: X → S be a smooth morphism in characteristic 0, and let (E, ∇X/S) be a relative regular connection. We define a cohomology of relative differential characters on X which receives classes of (E, ∇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 c2, the construction yields a connection of f_*c2(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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