Categories of complex variations of Hodge structure over compact K"ahler manifolds

Abstract

We give a complex polarized variation of Hodge structure over a compact K"ahler manifold $M$ which controls all finite-dimensional complex polarized variations of Hodge structure over $M$ and their tensor relations. As a corollary, we obtain the cohomology algebra with values in a local system admitting multiplicative Hodge structures.

12 pages. Comments welcome