Related papers: Self cup products and the theta characteristic tor…

Suppose $k$ is a finite field, that $C$ is a smooth projective geometrically irreducible curve over $k$, and that $n$ is a positive integer not divisible by the characteristic of $k$. In this paper we compute cup products of elements of the…

This paper is concerned with the theory of cup-products in Hopf-type cyclic cohomology of algebras and coalgebras. Here we give detailed proofs of the statements, announced in our previous paper. We show that the cyclic cohomology of a…

Let M be a Poisson manifold and A a Weil algebra. We describe an isomorphism of cohomolgy algebra and proves that Poisson cohomology with values in A is isomorphic to the tensor product of A with Poisson cohomolgy with real values.

In this paper, we compute the homology group and cohomology algebra of various polyhedral product objects uniformly from the point of view of diagonal tensor product. As applications, we introduce the polyhedral product method into…

We prove a formula for the cup product on the l-adic cohomology of the complement of a linear subspace arrangement.

We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This…

Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized…

This paper explores the cup and cap products within the cohomology and homology groups of ample groupoids, focusing on their applications and fundamental properties. Ample groupoids, which are \'etale groupoids with a totally disconnected…

Computing the cohomology of the tensor product of two vector bundles is central in the study of their moduli spaces and in applications to representation theory, combinatorics and physics. These computations play a fundamental role in the…

We find conditions such that cup products induce isomorphisms in low degrees for extensions between stable polynomial representations of the general linear group. We apply this result to prove generalizations and variants of the Steinberg…

We study the non-abelian Hopf cohomology theory of Radford products with coefficients in a comodule algebra. We show that these sets can be expressed in terms of the non-abelian Hopf cohomology theory of each factor of the Radford product.…

In this paper, we study the cup products and Betti numbers over cohomology superspaces of two-step nilpotent Lie superalgebras with coefficients in the adjoint modules over an algebraically closed field of characteristic zero. As an…

In this note we give formulas for cup product in Tate cohomology in terms of inhomogeneous cochains. Using one of these formulas, for a torus T defined over a non-archimedean local field K and splitting over a cyclic extension of K, we…

We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a ``cohomology theory" for complex algebraic varieties. The theory is bigraded, functorial,…

Let k be a field, q in k. We derive a cup product formula on the Hochschild cohomology ring of a family Lambda_q of quiver algebras. Using this formula, we determine a subalgebra of k[x,y] isomorphic to Hochschild cohomology modulo N, where…

In this paper we study the category LCA(2) of certain non-locally compact abelian topological groups, and extend the notion of Weil index. As applications we deduce some product formulas for curves over local fields and arithmetic surfaces.

We study cup product and cap product in Tate-Hochschild theory for a finite dimensional Frobenius algebra. We show that Tate-Hochschild cohomology ring equipped with cup product is isomorphic to singular Hochschild cohomology ring…

A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. In this paper, we define a cup product on the cohomology of a hom-associative algebra. We show that the cup product together with the degree…

We associate to each algebraic variety defined over $\mathbb{R}$ a filtered cochain complex, which computes the cohomology with compact supports and $\mathbb{Z}\_2$-coefficients of the set of its real points. This filtered complex is…

Let M be a paracompact smooth manifold of dimension n; A a Weil algebra and M^A the Weil bundle associated. We define and describe the notion of \widetilded-Poisson cohomology and of \widetilded^A -Poisson cohomology on M^A.