FROBENIUS ACTIONS ON LOCAL COHOMOLOGY MODULES AND DEFORMATION

Frobenius actions on the de Rham cohomology of Drinfeld modules

We study the action of endomorphisms of a Drinfeld A-module φ on its de Rham cohomology HDR(φ,L) and related modules, in the case where φ is defined over a field L of finite Acharacteristic p. Among others, we find that the nilspace H0 of the total Frobenius FrDR on HDR(φ,L) has dimension h = height of φ. We define and study a pairing between the p-torsion pφ of φ and HDR(φ,L), which becomes pe...

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...

Associated primes of local cohomology modules and Frobenius powers

We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include hypersurfaces of characteristic zero with rational singularities, as well as F-regular hypersurfaces of positive characteristic. As a consequence, we answer a question on the associated primes of certain families of ideals which arose from the localization problem in tight clos...

Associated primes of local cohomology modules and of Frobenius powers

We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include unique factorization domains of characteristic zero with rational singularities, as well as F-regular unique factorization domains of positive characteristic. As a consequence, we answer a question on the associated primes of Frobenius powers of ideals, which arose from the loc...

On Reducing sequences and an Application to Local Cohomology Modules