On de Rham Cohomology of Linear Categories

Details On de Rham Cohomology of Linear Categories On de Rham Cohomology of Linear Categories

2011-12-18

arxiv.org/abs/1112.4182v1

Mathematics

K-Theory and Homology

12 pages

Scientific paper

We define the Chern map from the Grothendieck group of a linear category C to
the de Rham cohomology of C with coefficients in a DG-category. In order to
achieve our goal, we define the notion of connection on a C-module, and we show
that the trace of the curvature of a connection is a de Rham cocycle, whose
cohomology class does not depend on the choice of the connection.

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