Triangulated categories of singularities and equivalences between Landau-Ginzburg models

The existence of a certain type of equivalence between triangulated categories of singularities for varieties of different dimensions is proved. This class of equivalences generalizes the so-called Knorrer periodicity. As a consequence, equivalences between the categories of D-branes of type B on Landau-Ginzburg models of different dimensions are obtained.

[1]  R. Hartshorne Residues And Duality , 1966 .

[2]  Peter Gabriel,et al.  Calculus of Fractions and Homotopy Theory , 1967 .

[3]  A. Grothendieck,et al.  Th'eorie des intersections et th'eor`eme de Riemann-Roch , 1971 .

[4]  R. Thomason Equivariant resolution, linearization, and Hilbert's fourteenth problem over arbitrary base schemes , 1987 .

[5]  Mikhail Kapranov,et al.  REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS , 1990 .

[6]  R. Thomason,et al.  Higher Algebraic K-Theory of Schemes and of Derived Categories , 1990 .

[7]  Masaki Kashiwara,et al.  Sheaves on Manifolds , 1990 .

[8]  D. Orlov,et al.  PROJECTIVE BUNDLES, MONOIDAL TRANSFORMATIONS, AND DERIVED CATEGORIES OF COHERENT SHEAVES , 1993 .

[9]  A. Bondal,et al.  Semiorthogonal decompositions for algebraic varieties. , 1995 .

[10]  Maxim Kontsevich,et al.  Homological Algebra of Mirror Symmetry , 1994, alg-geom/9411018.

[11]  S. I. Gelʹfand,et al.  Methods of Homological Algebra , 1996 .

[12]  Bernhard Keller,et al.  Derived Categories and Their Uses , 1996 .

[13]  D-Branes And Mirror Symmetry , 2000, hep-th/0005247.

[14]  Cumrun Vafa,et al.  Mirror Symmetry , 2000, hep-th/0002222.

[15]  Michael R. Douglas D-branes, categories and N=1 supersymmetry , 2000 .

[16]  P. Seidel Vanishing Cycles and Mutation , 2000, math/0007115.

[17]  B. Totaro The resolution property for schemes and stacks , 2002, math/0207210.

[18]  D branes in Landau-Ginzburg models and algebraic geometry , 2002, hep-th/0210296.

[19]  Dmitri Orlov Triangulated categories of singularities and D-branes in Landau-Ginzburg models , 2003 .

[20]  A. Kuznetsov Homological projective duality , 2005, math/0507292.

[21]  Pu Zhang,et al.  Triangulated Categories , 2021, Homological Theory of Representations.