Related papers: The strong Spector-Gandy Theorem for the higher an…

We posit that $d_n^2 < 2p_{n+1}$ holds for all $n\geq 1$, where $p_n$ represents the $n$th prime and $d_n$ stands for the $n$th prime gap i.e. $d_n := p_{n+1} - p_n$. Then, the presence of a prime between successive perfect squares, as well…

We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and…

We prove that if $P(X) \in \mathbb{Z}[X]$ is an integer polynomial of degree $n$ and having $P(0) = 1$, then either $P(X)$ is a product of cyclotomic polynomials, or else at least one of the complex roots of $P$ belongs to the disk $|z|…

The purpose of this paper is to define for every Polish space $X$ a class of sets, the $EBP(X)$-sets or the extended Baire property sets, to work out many properties of the $EBP(X)$-sets and to show their usefulness in analysis. For…

The subject of the present paper is Grothendieck's Lefschetz standard conjecture $B(X)$. Our main result is that, if $X$ is a projective smooth variety of dimension $n$ and the conjecture $B({\cal Y})$ holds for the generic fibre ${\cal Y}$…

Reider's Theorem on the very ampleness of adjoint linear series on a complex projective algebraic surface is extended in two new directions. First, Reider-type inequalities are shown to imply nefness of linear series of the form dH - E on…

Let X be an algebraic curve over Q and t a non-constant Q-rational function on X such that Q(t) is a proper subfield of Q(X). For every integer n pick a point P_n on X such that t(P_n)=n. We conjecture that, for large N, among the number…

A theorem of B. Green states that if A is a Dedekind ring whose fraction field is a local or global field, every normal projective curve over Spec(A) has a finite morphism to P^1_A. We give a different proof of a variant of this result…

In this paper we prove a generalization of a theorem of Schneider, which gives a criterion for a projective surface over the complex numbers to have an ample cotangent bundle. After reviewing different notions of positivity, we introduce a…

All spaces below are Tychonov. We define the projective pi-character p(X) of a space X as the supremum of the values $\pi\chi(Y)$ where Y ranges over all continuous images of X. Our main result says that every space X has a pi-base whose…

We show that the strongly symmetric spectral convex compact sets are precisely the normalized state spaces of finite-dimensional simple Euclidean Jordan algebras and the simplices. Spectrality is the property that every state has a convex…

We give necessary and sufficient conditions for the embeddings $\Lambda\text{BV}^{(p)}\subseteq \Gamma\text{BV}^{(q_n\uparrow q)}$ and $\Phi\text{BV}\subseteq\text{BV}^{(q_n\uparrow q)}$. As a consequence, a number of results in the…

A Banach space is {\it polynomially Schur} if sequential convergence against analytic polynomials implies norm convergence. Carne, Cole and Gamelin show that a space has this property and the Dunford-Pettis property if and only if it is…

In this note, we study various measures of irrationality for hypersurfaces in projective spaces which were recently proposed by Bastianelli, De Poi, Ein, Lazarsfeld and Ullery. In particular, we answer the question raised by Bastianelli…

The concern of this paper is to show that there always exist Krasner hyperfields of order n, where n is an integer greater than or equal to 2.

We investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\to\mathbb R$ which is…

This is a revised version of the second half of my paper math.AG/9909021. We prove that there exists a positive integer $\nu_{n}$ depending only on $n$ such that for every smooth projective $n$-fold of general type $X$ defined over complex…

We compute the algebraic Picard group of the category of $K(n)$-local spectra, for all heights $n$ and all primes $p$. In particular, we show that it is always finitely generated over $\mathbb{Z}_p$ and, whenever $n \geq 2$, is of rank $2$,…

We prove the analogue of the Martingale Convergence Theorem for polynomial spline sequences. Given a natural number $k $ and a sequence $(t_i)$ of knots in $[0,1]$ with multiplicity $\le k-1$, we let $P_n $ be the orthogonal projection onto…

We prove the following results. 1. If $X$ is a $\alpha$-favourable space, $Y$ is a regular space, in which every separable closed set is compact, and $f:X\times Y\to\mathbb R$ is a separately continuous everywhere jointly discontinuous…