For any smooth projective variety X of dimension n over an algebraically closed field k of characteristic p > 0 with μ(Ω X ) > 0. If T(Ω X ) (0 < l < n(p − 1)) are semi-stable, then the sheaf B X of exact 1-forms is stable. When X is a surface with μ(Ω X ) > 0 and Ω X is semi-stable, the sheaf B X of exact 2-forms is also stable. Moreover, under the same condition, the sheaf Z X of closed 1-for...

Type FPs A group Γ is of type FPs if Z, regarded as a ZΓ–module via the trivial action, admits a partial projective resolution Ps → Ps−1 → · · · → P1 → P0 → Z→ 0 by finitely generated ZΓ–modules Pi . Every group is of type FP0 . Type FP1 is equivalent to the property of finite generation. Every finitely-presented group is of type FP2 , but Bestvina–Brady showed the converse does not hold in gen...

This paper aims to study some semi-symmetric and curvature tensor conditions on α-Kenmotsu pseudo-metric manifolds. Some of semi-symmetric, locally symmetric, the Ricci are considered such Also, relationships between M-projective conformal tensor, concircularly conharmonic investigated. Finally, an example structure is given.

Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square order, then N must act semi-regularly on P. In addition we prove that if a finite non-Desarguesian projective plane P admits more than one nilpotent group which is regular on the points of P then P has non-square order a...

Among all complex projective varieties X →֒ P(V ), the equivarient embeddings of homogeneous varieties—those admitting a transitive action of a semi-simple complex algebraic group G—are the easiest to study. These include projective spaces, Grassmannians, non-singular quadrics, Segre varieties, and Veronese varieties. In Joe Harris’ book “Algebraic Geometry: A First Course” [H], he computes the ...

Let R be a unital semi-simple commutative complex Banach algebra, and let M(R) denote its maximal ideal space, equipped with the Gelfand topology. Sufficient topological conditions are given on M(R) for R to be a projective free ring, that is, a ring in which every finitely generated projective R-module is free. Several examples are included, notably the Hardy algebra H∞(X) of bounded holomorph...

Let L be the function field of a projective space P n k over an algebraically closed field k of characteristic zero, and H be the group of projective transformations. An H-sheaf V on P n k is a collection of isomorphisms V −→ g * V for each g ∈ H satisfying the chain rule. We construct, for any n > 1, a fully faithful functor from the category of finite-dimensional L-semi-linear representations...

Let L be the function field of a projective space P n k over an algebraically closed field k of characteristic zero, and H be the group of projective transformations. An H-sheaf V on P n k is a collection of isomorphisms V −→ g * V for each g ∈ H satisfying the chain rule. We construct, for any n > 1, a fully faithful functor from the category of finite-dimensional L-semi-linear representations...

We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves over a semi-separated noetherian scheme, generalising complete flat resolutions over a ring. By studying these complexes as objects of the pure derived category of flat sheaves we extend several results about totally acyclic complexes of projective modules to schemes; for example, we prove that a scheme is Goren...

LetX be an n-dimensional algebraic variety over a field of characteristic zero. We describe algebraically defined Deligne 1-motives Alb(X), Alb−(X), Pic(X) and Pic−(X) which generalize the classical Albanese and Picard varieties of a smooth projective variety. We compute Hodge, l-adic and De Rham realizations proving Deligne’s conjecture for H, H2n−1, H 1 and H1. We investigate functoriality, u...