Let L be a completely valued nonarchimedean field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) agrees with its Arens-Michael envelope and, furthermore, is a stably flat completion of its universal enveloping algebra. As an application, we prove that the Taylor relative cohomology for the locally convex algebra F(g) is naturally isomorphic to the L...

We give a simplified derivation of the expression of instanton numbers and of mirror map in terms of Frobenius map on p-adic cohomology and use this expression to prove integrality theorems. Modifying this proof we verify that the Aganagic-Vafa formulas for the number of holomorphic disks can be expressed in terms of Frobenius map on p-adic relative cohomology; this expression permits us to pro...

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existing algorithm for persistent homology to process any of the four modules, and relate it to a recently introduc...

Let A be a separable algebra (with an involution). The varieties of flags of (isotropic) ideals of A are considered and certain decompositions of these varieties in the category of Chow-correspondences are produced. As a consequence, decompositions in various cohomology theories are obtained.

We show that Melrose’s divisor flow and its generalizations by Lesch and Pflaum are invariants of K-theory classes for algebras of parametric pseudodifferential operators on a closed manifold, obtained by pairing the relative K-theory modulo the symbols with the cyclic cohomological character of a relative cycle constructed out of the regularized operator trace together with its symbolic bounda...

Let M be a complex projective manifold of dimension n+1 and f a meromorphic function on M obtained by a generic pencil of hyperplane sections of M . The n-th cohomology vector bundle of f0 = f |M−R, where R is the set of indeterminacy points of f , is defined on the set of regular values of f0 and we have the usual Gauss-Manin connection on it. Following Brieskorn’s methods in [Br], we extend t...

let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigate some properties of formal local cohomology modules with respect to a serre subcategory. we provide a common language to indicate some properties of formal local cohomology modules. let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigat...

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...