Eisenbud, David.
Minimal Free Resolutions over Complete Intersections [electronic resource] / by David Eisenbud, Irena Peeva. - 1st ed. 2016. - X, 107 p. online resource. - 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.
9783319264370
10.1007/978-3-319-26437-0 doi
Commutative algebra.
Commutative rings.
Algebraic geometry.
Category theory (Mathematics).
Homological algebra.
Mathematical physics.
Commutative Rings and Algebras.
Algebraic Geometry.
Category Theory, Homological Algebra.
Theoretical, Mathematical and Computational Physics.
QA251.3
512.44
Minimal Free Resolutions over Complete Intersections [electronic resource] / by David Eisenbud, Irena Peeva. - 1st ed. 2016. - X, 107 p. online resource. - 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.
9783319264370
10.1007/978-3-319-26437-0 doi
Commutative algebra.
Commutative rings.
Algebraic geometry.
Category theory (Mathematics).
Homological algebra.
Mathematical physics.
Commutative Rings and Algebras.
Algebraic Geometry.
Category Theory, Homological Algebra.
Theoretical, Mathematical and Computational Physics.
QA251.3
512.44