Related papers: Local cohomology -- an invitation
The aim of this paper is to construct and examine three candidates for local-to-global spectral sequences for the cohomology of diagrams of algebras with directed indexing. In each case, the $E^2$ -terms can be viewed as a type of local…
This article, intended for a general mathematical audience, is an informal review of some of the many interesting links which have developed between quantum cohomology and "classical" mathematics. It is based on a talk given at the Autumn…
This article is an overview of the geometrization conjecture for the local Langlands correspondence formulated by the author.
Let $\mathcal{A}$ be a locally noetherian Grothendieck category. In this paper we define and study the section functor on $\mathcal{A}$ with respect to an open subset of ASpec$\mathcal{A}$. Next we define and study local cohomology theory…
This article provides a concise introduction to Bartnik's quasi-local mass, and surveys a selection of results pertaining to the understanding of it. The aim is to serve as both an entry point to the topic, and a quick reference of results…
This is an example on the cohomology of threefolds.
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
This paper is a survey about recent developments in the local entropy theory for topological dynamical systems and continuous group actions, with particular emphasis on the connections with other areas of dynamical systems and mathematics.
We study loop near-rings, a generalization of near-rings, where the additive structure is not necessarily associative. We introduce local loop near-rings and prove a useful detection principle for localness.
We construct an arithmetic analogue of the quantum local systems on the moduli of curves, and study its basic structure. Such an arithmetic local system gives rise to a uniform way of assigning a Galois cohomology class of the first…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
We define and study the invariant linear and nonlinear horizontal double complexes of a local Lie group.
A systematic study of the contributions at infinity for the cohomology of variations of polarized Hodge structures over quasicompact K\"ahler manifolds. Several isomorphisms between different cohomologies given.
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
We define a new cohomology for associative algebras which we compute for algebras with units.
This chapter amalgamates some foundational developments and calculations in factorization homology.
Local cohomology techniques in equivariant homotopy theory, introduced by John Greenlees, may be applied to understand homology of classifying spaces through other equivariant data. In this paper we relate the local cohomology filtration to…
In this paper we give a geometric cobordism description of smooth integral cohomology. This model allows for simple descriptions of both the cup product and the integration, so that it is easy to verify the compatibilty of these structures.
We survey our works on the locally analytic vectors of completed cohomology of modular curves.
The aim of this paper is to define the structure of a ring on a graded cohomology group of a precubical set in coefficients in a ring with unit.