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Eisenbud, David

Minimal free resolutions over complete intersections - Cham, Switzerland: Springer, 2016 - x; 107p. pb; 20 cm - Lecture notes in mathematics, 0075-8434 ; Vol.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

Subjects--Topical Terms:
Mathematical and Computational Physics
Commutative Rings and Algebras.
Algebra, Homological.
Algebra
Physical Sciences &​ Mathematics
Mathematics
Physics
Category Theory, Homological Algebra.
Commutative Algebra.
Theoretical
Resolvents (Mathematics)
Algebra
Mathematical Physics
Algebraic Geometry
Mathematics -- Algebra -- Abstract.
Science -- Mathematical Physics
Mathematical Foundations
Syzygies (Mathematics)
Mathematics -- Geometry -- Algebraic.

Dewey Class. No.: 512.44 EIS