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Equivariant Hodge theory
and noncommutative geometry
Daniel Halpern-Leistner and Daniel Pomerleano |
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Geometry & Topology 24 (2020) 2361–2433
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Abstract |
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We develop a version of Hodge theory for a large class of smooth formally proper quotient stacks analogous to Hodge theory for smooth projective schemes. We show that the noncommutative Hodge–de 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 –theory of with respect to a maximal compact subgroup of , equipping the latter with a canonical pure Hodge structure. We also establish Hodge–de Rham degeneration for categories of matrix factorizations for a large class of equivariant Landau–Ginzburg models. |
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Keywords
$K$–theory, Hochschild homology, Hodge structures, derived
categories, equivariant geometry
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Mathematical Subject Classification 2010
Primary: 14A22, 14C30, 19D55, 19L47
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References |
Publication
Received: 9 November 2018
Revised: 20 October 2019
Accepted: 1 January 2020
Published: 29 December 2020
Proposed: Richard P Thomas
Seconded: Dan Abramovich, Frances Kirwan
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Authors |
| Daniel Halpern-Leistner | |
| Mathematics Department Cornell University Ithaca, NY United States |
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| Daniel Pomerleano | |
| Mathematics Department University of Massachusetts Boston Boston, MA United States |
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