Bockstein cohomology of associated graded rings

الأصل · EN

Let (A,m) be a Cohen-Macaulay local ring of dimension d and let I be an m-primary ideal. Let G be the associated graded ring of A I and let = A[It,t⁻¹] be the extended Rees ring of A with respect to I. Notice t⁻¹ is a non-zero divisor on and /t⁻¹ = G. So we have Bockstein operators βⁱ HⁱG₊(G)(-1) Hⁱ⁺¹G₊(G) for i ≥ 0. Since βⁱ⁺¹(+1)∘ βⁱ = 0 we have Bockstein cohomology modules BHⁱ(G) for i = 0,,d. In this paper we show that certain natural conditions on I implies vanishing of some Bockstein cohomology modules.