Abstract | Keywords | Export | Availability | Bookmark

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Algebra --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Algebraic geometry. --- Category theory (Mathematics). --- Homological algebra. --- Commutative algebra. --- Commutative rings. --- Physics. --- Commutative Rings and Algebras. --- Algebraic Geometry. --- Category Theory, Homological Algebra. --- Theoretical, Mathematical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Rings (Algebra) --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebraic geometry --- Geometry --- Math --- Science --- Algebra. --- Geometry, algebraic. --- Mathematical analysis --- Syzygies (Mathematics) --- Resolvents (Mathematics) --- Geometry, Algebraic. --- Syzygy theory (Mathematics) --- Categories (Mathematics) --- Resolvent of an operator --- Matrices --- Operator theory --- Mathematical physics. --- Physical mathematics --- Physics --- Algebra, Homological.