Equivalences of derived factorization categories of gauged Landau-Ginzburg models

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• 作者：Yuki Hirano ^{yuki-hirano@ed.tmu.ac.jp}
• 关键词：Derived categories ; Derived factorization categories ; Gauged Landau&ndash ; Ginzburg models ; Comodules over comonads
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：14 January 2017
• 年：2017
• 卷：306
• 期：Complete
• 页码：200-278
• 全文大小：942 K
• 卷排序：306

文摘

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.