Let X be a compact Kähler manifold of dimension n. For 1 ⩽ j m , let T closed positive (1,1)-current on whose cohomology class is Kähler. current bi-degree ( p ) with + n . We prove that if … are T-relative full mass intersection, then the non-pluripolar product equal to Dinh–Sibony

Introduction 2 1. Preliminaries on conformal algebras and modules 4 2. Basic definitions 9 3. Extensions and deformations 13 4. Homology 17 5. Exterior multiplication, contraction, and module structure 18 6. Cohomology of conformal algebras and their annihilation Lie algebras 19 6.1. Cohomology of the basic complex 19 6.2. Cohomology of the reduced complex 21 6.3. Cohomology of conformal algebr...

Kumar described the Schubert classes which are the dual to the closures of the Bruhat cells in the flag varieties of the Kac-Moody groups associated to the infinite dimensional KacMoody algebras [17]. These classes are indexed by affine Weyl groups and can be chosen as elements of integral cohomologies of the homogeneous space L̂polGC/B̂ for any compact simply connected semisimple Lie groupG. Lat...

In this paper, first we give the notion of a representation relative Rota-Baxter Lie algebra and introduce cohomologies with coefficients in representation. Then classify abelian extensions algebras using second cohomology group, skeletal 2-algebras third group as applications. At last, established general framework representations algebras, which is consistent associative literature, Applicati...

let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

We give short new geometric proofs of theorems of Bogley and Pride and of Serre. Both follow quickly from a global fixed point theorem. The Bogley–Pride theorem concerns aspherical relative group presentations and was applied in [5] to the multivariable adjunction problem. Serre’s theorem is a basic result concerning group cohomology and finite subgroups.

Let Γg,n, for 2g − 2 + n > 0, be the Teichmüller group of an n-punctured genus g compact Riemann surface Sg,n and let Γ(l), for a prime l ≥ 2, be the abelian level defined by the kernel of the natural representation Γg,n → Sp2g(Z/l). The pro-l completion Γ(l)(l) of Γ(l) defines a profinite completion of Γg,n, which we call the relative pro-l completion and denote by Γ (l) g,n. There is a natura...

We prove that if G is a countable, discrete group having infinite, normal subgroups with the relative property (T), then the Bernoulli shift action ofG on Π g∈G (X0, μ0)g for (X0, μ0) an arbitrary probability space, has first cohomology group isomorphic to the character group of G.