Kavli Affiliate: Yukinobu Toda
| First 5 Authors: Yalong Cao, Yukinobu Toda, Gufang Zhao, ,
| Summary:
Given a regular function $phi$ on a smooth stack, and a $(-1)$-shifted
Lagrangian $M$ on the derived critical locus of $phi$, under fairly general
hypotheses, we construct a pullback map from the Grothendieck group of coherent
matrix factorizations of $phi$ 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.
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