TY  - BOOK
AU  - Eisenbud,David
AU  - Peeva,Irena
TI  - Minimal free resolutions over complete intersections
T2  - Lecture notes in mathematics
SN  - 9783319264363
U1  - 512.62 23
PY  - 2016///
CY  - Cham
PB  - Springer
KW  - Syzygies (Mathematics)
KW  - Free resolutions (Algebra)
N1  - Includes bibliographical references and index; 1. Introduction and Survey --
2. Matrix Factorizations of One Element --
3. Finite Resolutions of HMF Modules --
4. CI Operators --
5. Infinite Resolutions of HMF Modules --
6. Far-Out Syzygies --
7. The Gorenstein Case --
8. Functoriality
N2  - 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
ER  -