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Nonabelian mixed Hodge structures
, 2000
"... Abstract — We propose a definition of “nonabelian mixed Hodge structure ” together with a construction associating to a smooth projective variety X and to a nonabelian mixed Hodge structure V, the “nonabelian cohomology of X with coefficients in V ” which is a (pre-)nonabelian mixed Hodge structure ..."
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Abstract — We propose a definition of “nonabelian mixed Hodge structure ” together with a construction associating to a smooth projective variety X and to a nonabelian mixed Hodge structure V, the “nonabelian cohomology of X with coefficients in V ” which is a (pre-)nonabelian mixed Hodge structure denoted H = Hom(XM, V). We describe the basic definitions and then give some conjectures saying what is supposed to happen. At the end we compute an example: the case where V has underlying homotopy type the complexified 2-sphere, and mixed Hodge structure coming from its identification with P 1. For
