$K$-theoretic pullbacks for Lagrangians on derived critical loci
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910865108762624 |
|---|---|
| author | Cao, Yalong Toda, Yukinobu Zhao, Gufang |
| author_facet | Cao, Yalong Toda, Yukinobu Zhao, Gufang |
| contents | Given a regular function $ϕ$ on a smooth stack, and a $(-1)$-shifted Lagrangian $M$ on the derived critical locus of $ϕ$, under fairly general hypotheses, we construct a pullback map from the Grothendieck group of coherent matrix factorizations of $ϕ$ to that of coherent sheaves on $M$. This map satisfies a functoriality property with respect to the composition of Lagrangian correspondences, as well as the usual bivariance and base-change properties.
We provide three applications of the construction, one in the definition of quantum $K$-theory of critical loci (Landau-Ginzburg models), paving the way to generalize works of Okounkov school from Nakajima quiver varieties to quivers with potentials, one in establishing a degeneration formula for $K$-theoretic Donaldson-Thomas theory of local Calabi-Yau 4-folds, the other in confirming a $K$-theoretic version of Joyce-Safronov conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $K$-theoretic pullbacks for Lagrangians on derived critical loci Cao, Yalong Toda, Yukinobu Zhao, Gufang Algebraic Geometry High Energy Physics - Theory Given a regular function $ϕ$ on a smooth stack, and a $(-1)$-shifted Lagrangian $M$ on the derived critical locus of $ϕ$, under fairly general hypotheses, we construct a pullback map from the Grothendieck group of coherent matrix factorizations of $ϕ$ to that of coherent sheaves on $M$. This map satisfies a functoriality property with respect to the composition of Lagrangian correspondences, as well as the usual bivariance and base-change properties. We provide three applications of the construction, one in the definition of quantum $K$-theory of critical loci (Landau-Ginzburg models), paving the way to generalize works of Okounkov school from Nakajima quiver varieties to quivers with potentials, one in establishing a degeneration formula for $K$-theoretic Donaldson-Thomas theory of local Calabi-Yau 4-folds, the other in confirming a $K$-theoretic version of Joyce-Safronov conjecture. |
| title | $K$-theoretic pullbacks for Lagrangians on derived critical loci |
| topic | Algebraic Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.06025 |