AI 中文总结
针对拟射影复簇\(Y\)及正则函数\(w\)，构建从\(w\)矩阵分解范畴的格罗滕迪克群到其临界上同调群的陈类特征，经拓扑\(K -\)理论群分解，证明相关定理并验证函子性质。
AI 中文摘要
对于拟射影复簇\(Y\)以及正则函数\(w \colon Y \to \mathbb C\)，我们构建了一个从\(w\)的矩阵分解范畴的格罗滕迪克群到\(w\)的临界上同调群的陈类特征，并表明它可通过某个拓扑\(K -\)理论群进行分解。我们证明了关于此陈类特征的格罗滕迪克 - 黎曼 - 罗赫定理，并验证了几个函子性质。
英文摘要
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.
Comments32 pages, comments welcome
