Local cohomology and base change

Equivariant Crystalline Cohomology and Base Change

Given a perfect field k of characteristic p > 0, a smooth proper k-scheme Y , a crystal E on Y relative to W (k) and a finite group G acting on Y and E, we show that, viewed as a virtual k[G]-module, the reduction modulo p of the crystalline cohomology of E is the de Rham cohomology of E modulo p. On the way we prove a base change theorem for the virtual Grepresentations associated with G-equiv...

TOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES

Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then there exists an ideal a of R such that AttR Hna (M)=T. As an application, we give some relationships between top local cohomology modules and top f...

On Base Change Theorem and Coherence in Rigid Cohomology

We prove that the base change theorem in rigid cohomology holds when the rigid cohomology sheaves both for the given morphism and for its base extension morphism are coherent. Applying this result, we give a condition under which the rigid cohomology of families becomes an overconvergent isocrystal. Finally, we establish generic coherence of rigid cohomology of proper smooth families under the ...

On Reducing sequences and an Application to Local Cohomology Modules

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...