All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 108

Showing per page

Sieve methods for varieties over finite fields and arithmetic schemes

Bjorn Poonen (2007)

Journal de Théorie des Nombres de Bordeaux

Classical sieve methods of analytic number theory have recently been adapted to a geometric setting. In the new setting, the primes are replaced by the closed points of a variety over a finite field or more generally of a scheme of finite type over ℤ . We will present the method and some of the surprising results that have been proved using it. For instance, the probability that a plane curve over 𝔽 2 is smooth is asymptotically 21 / 64 as its degree tends to infinity. Much of this paper is an exposition...

Slope filtration of quasi-unipotent overconvergent F -isocrystals

Nobuo Tsuzuki (1998)

Annales de l'institut Fourier

We study local properties of quasi-unipotent overconvergent F -isocrystals on a curve over a perfect field of positive characteristic p . For a φ - ∇ -module over the Robba ring ℛ , we define the slope filtration for Frobenius structures. We prove that an overconvergent F -isocrystal is quasi-unipotent if and only if it has the slope filtration for Frobenius structures locally at every point on the complement of the curve.

Small points on a multiplicative group and class number problem

Francesco Amoroso (2007)

Journal de Théorie des Nombres de Bordeaux

Let V be an algebraic subvariety of a torus 𝔾 m n ↪ ℙ n and denote by V * the complement in V of the Zariski closure of the set of torsion points of V . By a theorem of Zhang, V * is discrete for the metric induced by the normalized height h ^ . We describe some quantitative versions of this result, close to the conjectural bounds, and we discuss some applications to study of the class group of some number fields.

Solving an indeterminate third degree equation in rational numbers. Sylvester and Lucas

Tatiana Lavrinenko (2002)

Revue d'histoire des mathématiques

This article concerns the problem of solving diophantine equations in rational numbers. It traces the way in which the 19th century broke from the centuries-old tradition of the purely algebraic treatment of this problem. Special attention is paid to Sylvester’s work “On Certain Ternary Cubic-Form Equations” (1879–1880), in which the algebraico-geometrical approach was applied to the study of an indeterminate equation of third degree.

Currently displaying 21 – 40 of 108