Nonabelian mixed Hodge structures
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 $H=Hom(X_M, V)$. 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 2sphere, and mixed Hodge structure coming from its identification with $\pp ^1$. For this example we show that $Hom (X_M,V)$ is a namhs for any smooth projective variety $X$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2000
 arXiv:
 arXiv:math/0006213
 Bibcode:
 2000math......6213K
 Keywords:

 Algebraic Geometry
 EPrint:
 126 pages