Pushing forward matrix factorisations

TL;DR

This paper introduces a new method for pushing forward matrix factorizations along ring morphisms using Atiyah classes, and applies it to study convolution of kernels and derive a generalized Chern character formula.

Contribution

It presents a novel approach to pushforward of matrix factorizations with Atiyah classes and generalizes the Hirzebruch-Riemann-Roch formula for convolutions.

Findings

New formulation of pushforward using Atiyah classes

Elementary proof of Chern character formula for convolutions

Generalization of Hirzebruch-Riemann-Roch in this context

Abstract

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.