Standard conjecture D for matrix factorizations

  title={Standard conjecture D for matrix factorizations},
  author={Michael K. Brown and Mark E. Walker},
  journal={Advances in Mathematics},

Standard conjecture D for local stacky matrix factorizations

. We establish the non-commutative analogue of Grothendieck’s standard conjecture D for the differential graded category of G -equivariant matrix factorizations associated to an isolated hypersurface

A proof of a conjecture of Shklyarov

We prove a conjecture of Shklyarov concerning the relationship between K. Saito's higher residue pairing and a certain pairing on the periodic cyclic homology of matrix factorization categories.



Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations

We study the category of matrix factorizations for an isolated hypersurface singularity. We compute the canonical bilinear form on the Hochschild homology of this category. We find explicit

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A topological interpretation of Hochster's Theta pairing of two modules on a hypersurface ring is given in terms of linking numbers. This generalizes results of M. Hochster and proves a conjecture of

Non-commutative Hodge structures: Towards matching categorical and geometric examples

The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas

Adams Operations on Matrix Factorizations

We define Adams operations on matrix factorizations, and we show these operations enjoy analogues of several key properties of the Adams operations on perfect complexes with support developed by

A note on Grothendieck's standard conjectures of type C and D

Grothendieck conjectured in the sixties that the even Kunneth projector (with respect to a Weil cohomology theory) is algebraic and that the homological equivalence relation on algebraic cycles

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1. Gauss-Manin connection 2. Limit mixed Hodge structure on the vanishing cohomology of an isolated hypersurface singularity 3. The period map of a m-constant deformation of an isolated hypersurface