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Higher residues and canonical pairing on the twisted de Rham cohomology

Hoil Kim, Taejung Kim

Abstract

We describe an explicit formula of the canonical pairing on the twisted de Rham cohomology associated with the category of local matrix factorizations and by characterizing its relation to Saito's higher residue pairings, we reprove the conjecture of Shklyarov.

Higher residues and canonical pairing on the twisted de Rham cohomology

Abstract

We describe an explicit formula of the canonical pairing on the twisted de Rham cohomology associated with the category of local matrix factorizations and by characterizing its relation to Saito's higher residue pairings, we reprove the conjecture of Shklyarov.
Paper Structure (12 sections, 10 theorems, 86 equations)

This paper contains 12 sections, 10 theorems, 86 equations.

Table of Contents

  1. Introduction
  2. Outline of paper
  3. Local cohomology and higher residue pairings $\mathscr{H}_f$
  4. Local cohomology
  5. Higher residue pairings
  6. Equivalence between the canonical pairing and $(-1)^{\frac{n(n+1)}{2}}\mathscr{H}_f$.
  7. Characteristic equation of the canonical pairing
  8. The properties of Grothendieck's residue
  9. The equivalence
  10. Saito's higher residue pairings $\mathscr{K}_{f}$ and $u^n\mathscr{H}_f$.
  11. Equivalence
  12. The conjecture of Shklyarov

Key Result

Lemma 2.1

Theorems & Definitions (21)

  • Definition 1
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Theorem 3.1
  • ...and 11 more