# Minimal Free Resolutions over Complete Intersections

Eisenbud, David.

Minimal Free Resolutions over Complete Intersections by David Eisenbud, Irena Peeva. - New York: Springer, 2016. - X, 107 p. - Lecture Notes in Mathematics, 2152 0075-8434 ; . - Lecture Notes in Mathematics, 2152 .

This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.

ISBN: 9783319264363 (Pbk)

Standard No.: 10.1007/978-3-319-26437-0 doi

LCCN: 2019764671

Subjects--Topical Terms:

Algebraic geometry.

Category theory (Mathematics).

Commutative algebra.

Commutative rings.

Homological algebra.

Mathematical physics.

Commutative Rings and Algebras.

Algebraic Geometry.

Category Theory, Homological Algebra.

Theoretical, Mathematical and Computational Physics.

Dewey Class. No.: 512.62 Ei83M

Minimal Free Resolutions over Complete Intersections by David Eisenbud, Irena Peeva. - New York: Springer, 2016. - X, 107 p. - Lecture Notes in Mathematics, 2152 0075-8434 ; . - Lecture Notes in Mathematics, 2152 .

This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.

Algebraic geometry.

Category theory (Mathematics).

Commutative algebra.

Commutative rings.

Homological algebra.

Mathematical physics.

Commutative Rings and Algebras.

Algebraic Geometry.

Category Theory, Homological Algebra.

Theoretical, Mathematical and Computational Physics.