nLab
Koszul-Tate resolution

Skip the Navigation Links | Home Page | All Pages | Recently Revised | Authors | Feeds | Export |

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Contents

Idea

For A an algebra and I⊂A an ideal, a Koszul-Tate resolution is a resolution of the quotient A/I by a cochain dg-algebra in non-positive degree that is degreewise free/projective.

It is a refinement of a Koszul complex or rather an extension.

Applications

References

  • Jean-Louis Koszul, Homologie et cohomologie des algèbres de Lie , Bulletin de la Société Mathématique de France, 78, 1950, pp 65-127.

  • John Tate, Homology of Noetherian rings and local rings , Illinois Journal of Mathematics, 1, 1957, pp. 14-27

Revised on May 11, 2013 17:35:59 by Anonymous Coward (98.114.12.203)
Edit | Back in time (2 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: BV-BRST formalism, homological resolution, graded vector space, vector space, crossed complex, quasi-isomorphism, projective object, crossed module, A-infinity-category, Moore complex, 2-crossed module, crossed square, Dold-Kan correspondence, dg-category, Categories and Sheaves, kernel, cokernel, additive category, abelian category, exact functor, pre-additive category, additive and abelian categories, homological algebra, chain complex, category with translation, derived category, triangulated category, homology, differential, category of chain complexes, Quillen exact category, differential graded algebra, Grothendieck category, complex, injective object, differential graded coalgebra, semi-abelian category, double complex, bar and cobar construction, satellite, additive functor, homological perturbation theory, exact sequence, element in an abelian category, flat module, Gabriel multiplication, Serre subcategory, differential forms on simplices, enhanced triangulated category, pretriangulated dg-category, twisted complex, Grothendieck spectral sequence, spectral sequence, Hochschild-Serre spectral sequence, snake lemma, model structure on chain complexes, chain homology and cohomology, semifree dga, monoidal Dold-Kan correspondence, differential crossed module, de Rham theorem, Eilenberg-Zilber theorem, homotopically injective object, free module, five lemma, stable derivator, stable model category, An Introduction to Homological Algebra, Koszul complex, hypercrossed complex, phase space, split exact sequence, projective module, universal coefficient theorem, Ext, Tor, homological algebra - contents, Freyd-Mitchell embedding theorem, connecting homomorphism, chain homotopy, spectral sequence of a filtered complex, Eilenberg-Zilber map, hyper-derived functor, singular homology, curved dg-algebra, bounded chain complex, Betti number, model structure on dg-modules, Koszul-Tate resolution, Quantization of Gauge Systems, Deligne conjecture, delta-functor, model structure on cosimplicial simplicial sets, dual vector space, contents of contents, Bridgeland stability condition, global dimension theorem, suspension of a chain complex, Bockstein homomorphism, 3x3 lemma, diagram chasing, Leray spectral sequence, relative homology, Jean-Louis Koszul, derived functor in homological algebra, syzygy, projective resolution, reduced homology, exact couple, null homotopy, ordinary homology, interval object in chain complexes, abelian subcategory, internal hom of chain complexes, Baer's criterion, tensr product of chain complexes, tensor product of chain complexes, horseshoe lemma, associated graded object, filtered chain complex, chain map, Adams spectral sequence, Serre spectral sequence, Bockstein spectral sequence, truncation of a chain complex, simplicial homology, (infinity,1)-category of chain complexes, exact triangle, total derived functor, flat resolution lemma, flat resolution, salamander lemma, compactly generated triangulated category, spectral sequence of a double complex, injective module, cellular homology, total complex, homotopy category of chain complexes, free resolution, elliptic chain complex, long exact sequence in homology, four lemma, Lazard's criterion, projector, connective chain complex