Koszul–Tate resolution

In mathematics, a Koszul–Tate resolution or Koszul–Tate complex of the quotient ring R/M is a projective resolution of it as an R-module which also has a structure of a dg-algebra over R, where R is a commutative ring and M ⊂ R is an ideal. They were introduced by Tate (1957) as a generalization of the Koszul resolution for the quotient R/(x₁, ...., x_n) of R by a regular sequence of elements. Friedemann Brandt, Glenn Barnich, and Marc Henneaux (2000) used the Koszul–Tate resolution to calculate BRST cohomology. The differential of this complex is called the Koszul–Tate derivation or Koszul–Tate differential.