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Standard conjecture D for local stacky matrix factorizations

Bumsig Kim, Taejung Kim

Abstract

We establish the non-commutative analogue of Grothendieck's standard conjecture D for the differential graded category of $G$-equivariant matrix factorizations associated to an isolated hypersurface singularity where $G$ is a finite group.

Standard conjecture D for local stacky matrix factorizations

Abstract

We establish the non-commutative analogue of Grothendieck's standard conjecture D for the differential graded category of -equivariant matrix factorizations associated to an isolated hypersurface singularity where is a finite group.
Paper Structure (17 sections, 7 theorems, 58 equations)

This paper contains 17 sections, 7 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. Outline of paper
  3. The Milnor fibration and the polarized mixed Hodge structure
  4. Milnor fibration and Brieskorn lattice
  5. Polarized mixed Hodge structure on $H^n(X_\infty; {\mathbb Q})$
  6. Higher residue pairings
  7. K. Saito's higher residue pairing
  8. Higher residue pairing associated with Hertling's polarization $S$
  9. $G$-equivariant theory
  10. Milnor fibration in the $G$-equivariant setting
  11. $G$-equivariant matrix factorizations
  12. The Grothendieck group
  13. Chern-character-type map $\mathrm{ch}_{X_\infty}$
  14. $G$-equivariant Hochschild Chern character $\mathrm{ch}^{G}_{\mathrm{HH}}$
  15. $G$-equivariant negative cyclic Chern character $\mathrm{ch}^{G}_{\mathrm{HN}}$
  16. ...and 2 more sections

Key Result

Proposition 2.3.12

BW2HertlingHe3

Theorems & Definitions (15)

  • Remark 2.1
  • Proposition 2.3.12
  • Definition 3.1
  • Proposition 3.5.12
  • Theorem 4.1
  • proof
  • Corollary 4.2
  • proof
  • Lemma 4.3
  • proof
  • ...and 5 more