Relative Algebraic Differential Characters

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 $f_{\ast }{c}_2(E)$. This one has been constructed analytically by A. Beilinson. We also relate our construction to the trace complex of Beilinson of Schechtman.

Latex 2e, 25 pages

References in corpus (1)

• Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman

Cited by in corpus (2)

• The Hitchin connection in arbitrary characteristic
• The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations