Bockstein Homomorphisms in Local Cohomology
نویسندگان
چکیده
Let R be a polynomial ring in finitely many variables over the integers, and fix an ideal a of R. We prove that for all but finitely prime integers p, the Bockstein homomorphisms on local cohomology, H a (R/pR) −→ H k+1 a (R/pR), are zero. This provides strong evidence for Lyubeznik’s conjecture which states that the modules H a (R) have a finite number of associated prime ideals.
منابع مشابه
On natural homomorphisms of local cohomology modules
Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$. Let $I$ be an ideal of $R$ with $grade(I,M)=c$. In this article we will investigate several natural homomorphisms of local cohomology modules. The main purpose of this article is to investigate when the natural homomorphisms $gamma: Tor^{R}_c(k,H^c_I(M))to kotim...
متن کاملBockstein Closed 2-Group Extensions and Cohomology of Quadratic Maps
A central extension of the form E : 0 → V → G → W → 0, where V and W are elementary abelian 2-groups, is called Bockstein closed if the components qi ∈ H ∗(W,F2) of the extension class of E generate an ideal which is closed under the Bockstein operator. In this paper, we study the cohomology ring of G when E is a Bockstein closed 2-power exact extension. The mod-2 cohomology ring of G has a sim...
متن کاملLow-Degree Cohomology of Integral Specht Modules
We introduce a way of describing cohomology of the symmetric groups Σn with coefficients in Specht modules. We study H (Σn, S λ R) for i ∈ {0, 1, 2} and R = Z, Fp. The focus lies on the isomorphism type of H(Σn, S λ Z ). Unfortunately, only in few cases can we determine this exactly. In many cases we obtain only some information about the prime divisors of |H(Σn, S λ Z )|. The most important to...
متن کاملRing structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
متن کاملThe Integral Cohomology of the Bianchi Groups
We calculate the integral cohomology ring structure for various members of the Bianchi group family. The main tools we use are the Bockstein spectral sequence and a long exact sequence derived from Bass-Serre theory.
متن کامل