标题： 拉格朗日函数在导出的临界轨迹上的 $K$ 理论拉回 显示英文标题

标题： $K$-theoretic pullbacks for Lagrangians on derived critical loci

摘要： 给定定义在光滑叠量上的正则函数$\phi$和定义在$\phi$的导出临界点簇上的$(-1)$- 平移拉格朗日子簇$M$，在相当一般的假设下，我们构造了一个从$\phi$的凝聚矩阵因子的 Grothendieck 群到$M$上凝聚层的 Grothendieck 群的拉回映射。 此映射在拉格朗日对应复合运算下满足函子性性质，同时也满足通常的双变性与基变换性质。 我们给出了该构造的三个应用：其中一个是在临界构型（Landau-Ginzburg 模型）的量子$K$-理论定义中，为将 Okounkov 学派的工作从 Nakajima 箭图簇推广到具有势的箭图铺平了道路；另一个是在局部 Calabi-Yau 4 折积的$K$-理论 Donaldson-Thomas 理论退化公式建立中；还有一个是在证实 Joyce-Safronov 猜想的$K$-理论版本中。 显示英文摘要

摘要： 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.