Desingulization of Quasi-smooth Derived Schemes and Virtual Fundamental Classes

Abstract

We prove a desingularization theorem for the quasi-smooth derived scheme, in the sense of Hekking. We also propose the conjecture that the K-theoretic integration of the virtual fundamental class of a quasi-smooth derived scheme could be explained as the K-theoretic integration of wedge powers of non-negative rank perfect complexes with Tor-amplitude [0,1] over smooth schemes.