Duke Mathematical Journal

Pushing forward matrix factorizations

Tobias Dyckerhoff and Daniel Murfet

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Abstract

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

Article information

Source
Duke Math. J., Volume 162, Number 7 (2013), 1249-1311.

Dates
First available in Project Euclid: 10 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1368193653

Digital Object Identifier
doi:10.1215/00127094-2142641

Mathematical Reviews number (MathSciNet)
MR3079249

Zentralblatt MATH identifier
1273.14014

Subjects
Primary: 18E30: Derived categories, triangulated categories
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]

Citation

Dyckerhoff, Tobias; Murfet, Daniel. Pushing forward matrix factorizations. Duke Math. J. 162 (2013), no. 7, 1249--1311. doi:10.1215/00127094-2142641. https://projecteuclid.org/euclid.dmj/1368193653


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