Equivalences of derived factorization categories of gauged Landau–Ginzburg models

Abstract

For a given Fourier–Mukai equivalence of bounded derived categories of coherent sheaves on smooth quasi-projective varieties, we construct Fourier–Mukai equivalences of derived factorization categories of gauged Landau–Ginzburg (LG) models.As an application, we obtain some equivalences of derived factorization categories of K-equivalent gauged LG models. This result is an equivariant version of the result of Baranovsky and Pecharich, and it also gives a partial answer to Segal's conjecture. As another application, we prove that if the kernel of the Fourier–Mukai equivalence is linearizable with respect to a reductive affine algebraic group action, then the derived categories of equivariant coherent sheaves on the varieties are equivalent. This result is shown by Ploog for finite groups case.