We identify the category of real mixed Hodge structures with the category of vector bundles with connections (not necessarily flat) on , equivariant with respect to . Here is the complex plane considered as a 2-dimensional real manifold, and is the multiplicative group of complex numbers considered as a real group.
Cite this article
Mikhail Kapranov, Real mixed Hodge structures. J. Noncommut. Geom. 6 (2012), no. 2, pp. 321–342DOI 10.4171/JNCG/93