For x₁, …, xₙ in a commutative ring R, the Koszul complex K_•(x; R) has K_p = Λ^p(R^n) with differential contracting by the vector (x₁, …, xₙ). If (x₁, …, xₙ) is a regular sequence, K_• is a free resolution of R/(x₁, …, xₙ), so Tor^R(R/x,…
For x₁, …, xₙ in a commutative ring R, the Koszul complex K_•(x; R) has K_p = Λ^p(R^n) with differential contracting by the vector (x₁, …, xₙ). If (x₁, …, xₙ) is a regular sequence, K_• is a free resolution of R/(x₁, …, xₙ), so Tor^R(R/x,…