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2020 Equivariant Hodge theory and noncommutative geometry
Daniel Halpern-Leistner, Daniel Pomerleano
Geom. Topol. 24(5): 2361-2433 (2020). DOI: 10.2140/gt.2020.24.2361

Abstract

We develop a version of Hodge theory for a large class of smooth formally proper quotient stacks XG 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 K–theory of X with respect to a maximal compact subgroup of G, 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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Daniel Halpern-Leistner. Daniel Pomerleano. "Equivariant Hodge theory and noncommutative geometry." Geom. Topol. 24 (5) 2361 - 2433, 2020. https://doi.org/10.2140/gt.2020.24.2361

Information

Received: 9 November 2018; Revised: 20 October 2019; Accepted: 1 January 2020; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194295
Digital Object Identifier: 10.2140/gt.2020.24.2361

Subjects:
Primary: 14A22 , 14C30 , 19D55 , 19L47

Keywords: $K$–theory , derived categories , equivariant geometry , Hochschild homology , Hodge structures

Rights: Copyright © 2020 Mathematical Sciences Publishers

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