Real non-abelian mixed Hodge structures for quasi-projective varieties: formality and splitting
Abstract
We define and construct mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. We also show that these split on tensoring with the ring R[x] equipped with the Hodge filtration given by powers of (x-i), giving new results even for simply connected varieties. The mixed Hodge structures can thus be recovered from the Gysin spectral sequence of cohomology groups of local systems, together with the monodromy action at the Archimedean place. As the basepoint varies, these structures all become real variations of mixed Hodge structure.
Keywords
Cite
@article{arxiv.1104.1409,
title = {Real non-abelian mixed Hodge structures for quasi-projective varieties: formality and splitting},
author = {J. P. Pridham},
journal= {arXiv preprint arXiv:1104.1409},
year = {2016}
}
Comments
139 pages; v2 is the concatenation of v1 (sections 10-13) and arXiv:0902.0770 (sections 1-9); v3 New section 1, and general reorganisation with some new material - final version, to appear in Mem. AMS