A topological Chern character for matrix factorizations

Mark Shoemaker

arXiv:2607.21788v1 Primary: math.AG Secondary: math-ph, math.AT

Abstract

For $Y$ a quasi-projective complex variety and $w \colon Y \to \mathbb C$ a regular function, we construct a Chern character from the Grothendieck group of the category of matrix factorizations of $w$ to the critical cohomology of $w$, and show that it factors through a certain topological $K$-theory group. We prove a Grothendieck-Riemann-Roch theorem with respect to this Chern character, and verify several functorial properties.

Disclosure

“6 SHOEMAKER 0.6. Statement on the use of AI. Gemini and ChatGPT were used to an- swer questions and search for references. All logical arguments, proofs, and writing are the author’s own. 0.7. Acknowledgements. I would like to thank Nicolas Addington, Michael Brown, David Favero, Tyler Kell”
PDF page 6

Classification: Literature search
Multiplier: 2
Verified: 2026-08-23T19:04:19.388501Z

Structural counts

Pages 32 pdf

Theorems 7 source

Lemmas 2 source

Propositions 6 source

Corollaries 5 source

Definitions 10 source

Displayed equations 167 source

Bibliography entries 44 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file Chern_character_7-20-26.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.