Related papers: Projectively simple rings

We give a categorical description of all abelian varieties with commutative endomorphism ring over a finite field with $q=p^a$ elements in a fixed isogeny class in terms of pairs consisting of a fractional $\mathbb Z[\pi,q/\pi]$-ideal and a…

We study the ring of sections A(X) of a complete symmetric variety X, that is of the wonderful completion of G/H where G is an adjoint semi-simple group and H is the fixed subgroup for an involutorial automorphism of G. We find generators…

We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and rings in which every right ideal is a finite direct sum of…

In this paper, we investigate automorphisms of compact K\"ahler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces X whose groups of…

We prove that for every reductive algebraic group $H$ with centre of positive dimension and every integer $K$ there is a smooth and projective variety $X$ and an algebraic $H$-torsor $P \to X$ such that the classifying map $X \to \Bclass H$…

Let X be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic different from two. If X admits a nontrivial automorphism \sigma that fixes pointwise all the order two…

We consider the following conjecture: if X is a smooth projective variety over a field of characteristic zero, then there is a dense set of reductions X_s of X to positive characteristic such that the action of the Frobenius morphism on the…

We characterise the virtually abelian groups which are fundamental groups of compact K\"ahler manifolds and of smooth projective varieties. We show that a virtually abelian group is K\"ahler if and only if it is projective. In particular,…

We study the groups of rational points of abelian varieties defined over a finite field $ \mathbb{F}_q$ whose endomorphism rings are commutative, or, equivalently, whose isogeny classes are determined by squarefree characteristic…

Given a projective scheme $X$ over a field $k$, an automorphism $\sigma$ of $X$, and a $\sigma$-ample invertible sheaf $L$, one may form the twisted homogeneous coordinate ring $B = B(X, L, \sigma)$, one of the most fundamental…

Given a group G, a (unital) ring A and a group homomorphism $\sigma : G \to \Aut(A)$, one can construct the skew group ring $A \rtimes_{\sigma} G$. We show that a skew group ring $A \rtimes_{\sigma} G$, of an abelian group G, is simple if…

For an extension A/B of neither necessarily associative nor necessarily unital rings, we investigate the connection between simplicity of A with a property that we call A-simplicity of B. By this we mean that there is no non-trivial ideal I…

We give a short new computation of the quantum cohomology of an arbitrary smooth toric variety $X$, by showing directly that the Kodaira-Spencer map of Fukaya-Oh-Ohta-Ono defines an isomorphism onto a suitable Jacobian ring. The proof is…

A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational…

Suppose that $X$ is a projective manifold whose tangent bundle $T_X$ contains a locally free strictly nef subsheaf. We prove that $X$ is isomorphic to a projective bundle over a hyperbolic manifold. Moreover, if the fundamental group…

This paper studies the multiplicative ideal structure of commutative rings in which every finitely generated ideal is quasi-projective. Section 2 provides some preliminaries on quasi-projective modules over commutative rings. Section 3…

Let $X$ be a projective and smooth variety over an algebraically closed field $k$. Let $f:Y\rightarrow X$ be a proper and surjective morphism of $k$-varieties. Assuming that $f$ is separable, we prove that the Tannakian category associated…

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring B(X, L, sigma), which is surjective in large degree. This…

Chevalley's theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian…

We consider the following conjecture: if X is a smooth projective variety over a field of characteristic zero, then there is a dense set of reductions X_s to positive characteristic such that the action of the Frobenius morphism on the top…