Pushing forward matrix factorizations

By Tobias Dyckerhoff, Daniel Murfet. 2011

47 citations recorded by the source corpus.

We describe the pushforward of a matrix factorisation along a ring morphism in terms of an idempotent defined using relative Atiyah classes, and use this construction to study the convolution of kernels defining integral functors between categories of matrix factorisations. We give an elementary proof of a formula for the Chern character of the convolution generalising the Hirzebruch-Riemann-Roch formula of Polishchuk and Vaintrob.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/412b886ddc0547f6700e32efb93e6ff2158c0a88

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Deformations of colored sl(N) link homologies via foams (2015, methodology): “This same method (which is adapted from the results in Dyckerhoff and Murfet [11]) shows that the stabilization result for the digon web follows provided the tensor product of Koszul complexes associated to the web only has homology in degree zero, and which equals the corresponding tensor product o”
Coherent analogues of matrix factorizations and relative singularity categories (2011, background): “There was some attention paid to pull-backs and push-forwards of matrix factorizations recently [Polishchuk and Vaintrob 2011; 2014; Dyckerhoff and Murfet 2013].”