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Minimal Free Resolutions over Complete Intersections

by Eisenbud, David; Peeva, Irena.
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 2152Publisher: New York: Springer, 2016Description: X, 107 p.ISBN: 9783319264363 (Pbk).Subject(s): 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 PhysicsDDC classification: 512.62 Ei83M Summary: 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.
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Reference Section
Reference 512.62 Ei83M (Browse shelf) Not For Loan Reserve 10881
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512.556 Si62F Finite von Neumann algebras and masas 512.556 Su72I Invitation to von Neumann algebras 512.6 Mc222H Homology 512.62 Ei83M Minimal Free Resolutions over Complete Intersections 512.66 K147K K-theory : 512.66 W424K K-book : 512.7 AN26R Ramanujan's lost notebook :

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.

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