Related papers: Local cohomology and D-affinity in positive charac…

This paper at first concerns some criteria on Artinianness and vanishing of formal local cohomology modules. Then we consider the cosupport and the set of coassociated primes of these modules more precisely.

We present a non-standard proof of the fact that the existence of a local (i.e. restricted to a point) characteristic-zero, semi-parametric lifting for a variety defined by the zero locus of polynomial equations over the integers is…

We establish Grauert--Riemenschneider vanishing for $F$-pure threefolds over a perfect field $k$ of characteristic $p>5$. We apply this to prove Steenbrink vanishing for three-dimensional sharply $F$-pure pairs in characteristic $p>5$. As a…

Let R be a commutative Noetherian ring. We introduce a theory of formal local cohomology for complexes of R-modules. As an application, we establish some relations between formal local cohomology, local homology, local cohomology and local…

We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces new classes of rigid and test modules, in particular over local…

This article contains a new argument which proves vanishing of the first cohomology for negative vector bundles over a complex projective variety if the rank of the bundle is smaller than the dimension of the base. Similar argument is…

A general vanishing result for the first cohomology group of affine smooth complex varieties with values in rank one local systems is established. This is applied to the determination of the monodromy action on the first cohomology group of…

We introduce a generalization of the notion of local homology module, which we call a local homology module with respect to a pair of ideals $\left(I,J\right)$, and study its various properties such as vanishing, co-support and…

We give a new perspective on the homological characterisations of amenability given by Johnson in the context of bounded cohomology and by Block and Weinberger in the context of uniformly finite homology. We examine the interaction between…

We give a short, geometric proof of Graham's theorem on positivity in the equivariant cohomology of a flag variety, based on a transversality argument.

Let R be a (not necessarily local) Noetherian ring and M a finitely generated R-module of finite dimension d. Let \fa be an ideal of R and \fM denote the intersection of all prime ideals \fp in Supp_RH^d_{\fa}(M). It is shown that…

We prove a relative Kawamata Viehweg vanishing type theorem for birational morphisms. We use this to prove a Grauert Riemenschneider theorem over log canonical threefolds without zero dimensional log canonical centers, in residue…

Bott vanishing is a strong vanishing result for the cohomology of exterior powers of the cotangent bundle twisted by ample line bundles. Buch-Thomsen-Lauritzen-Mehta conjectured that partial flag varieties (which are not products of…

We construct Landau-Ginzburg models for numerically effective complete intersections in toric manifolds as partial compactifications of families of Laurent polynomials. We show a mirror statement saying that the quantum D-module of the…

In all forms of the local Langlands program the abelian category of smooth representations of p-adic groups G in vector spaces over a field k plays a central role. Of particular interest are its finiteness properties. If the field k has…

The main focus of this paper is on determining the highest non-vanishing local cohomology modules of \Omega_(B/R), \Omega_(B/V)(\Omega_(B/k)) where R is either a complete regular local ring or a complete local normal domain with coefficient…

We prove that if M, N are finite modules over a Gorenstein local ring R of codimension at most 4, then the vanishing of Ext^n_R(M,N) for n\gg 0 is equivalent to the vanishing of Ext^n_R(N,M) for n\gg 0. Furthermore, if the completion of $R$…

Let $\fa$ denote an ideal of a $d$-dimensional Gorenstein local ring $R$ and $M$ and $N$ two finitely generated $R$-modules with $\pd M< \infty$. It is shown that $H^d_{\fa}(M,N)=0$ if and only if $\dim \hat{R}\big/ \fa\hat{R}+\fp>0$ for…

Let R be a commutative Noetherian d-dimensional complete equicharacterisitc regular local ring and let I be an ideal of R such that every minimal prime over I has height at most c. Let v=d - [(d-2)/c]-1 and v'=d - [(d-1)/c]. It has been…

In this paper we study the variability and rigidity of secondary characteristic classes which arise from flat connections on a manifold. Considering the connection as a Lie-algebra valued one-form, we study the characteristic map from Lie…