Matrix Factorizations and Knörrer Periodicity

Abstract: A matrix factorization of a ring element $f$ is a pair of square matrices so that the product (in either order) is diagonal with $f$ in each diagonal entry. These were introduced by David Eisenbud in 1980. When the ring is regular, matrix factorizations of $f$ correspond to maximal Cohen-Macaulay modules over the hypersurface defined by $f.$ This talk will give an overview of the theory of matrix factorizations, ending with some recent generalizations to factorizations by more than two matrices.

Mathematics

Audience: learners

IIT Bombay Virtual Commutative Algebra Seminar

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