Equivariant Hodge theory and noncommutative geometry
Abstract
We develop a version of Hodge theory for a large class of smooth formally proper quotient stacks $X/G$ analogous to Hodge theory for smooth projective schemes. We show that the noncommutative Hodgede Rham sequence for the category of equivariant coherent sheaves degenerates. This spectral sequence converges to the periodic cyclic homology, which we canonically identify with the topological equivariant Ktheory of $X$ with respect to a maximal compact subgroup of $G$, equipping the latter with a canonical pure Hodge structure. We also establish Hodgede Rham degeneration for categories of matrix factorizations for a large class of equivariant LandauGinzburg models.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 DOI:
 10.48550/arXiv.1507.01924
 arXiv:
 arXiv:1507.01924
 Bibcode:
 2015arXiv150701924H
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  KTheory and Homology;
 19L47;
 19D55;
 14A22;
 14C30
 EPrint:
 47 pages, updated to match the published version, to avoid confusion. Following referee's suggestion, we reorganized the paper so that all matrix factorization material appears in its own separate section