nLab
Koszul-Tate resolution

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 AA an algebra and IAI \subset A an ideal, a Koszul-Tate resolution is a resolution of the quotient A/IA/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)