EuDML | Browse

Items

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

Displaying 241 – 260 of 284

The modified diagonal cycle on the triple product of a pointed curve

Benedict H. Gross, Chad Schoen (1995)

Annales de l'institut Fourier

Let $X$ be a curve over a field $k$ with a rational point $e$ . We define a canonical cycle $Δ_{e} \in Z^{2} (X^{3})_{hom}$ . Suppose that $k$ is a number field and that $X$ has semi-stable reduction over the integers of $k$ with fiber components non-singular. We construct a regular model of $X^{3}$ and show that the height pairing $⟨ τ_{*} (Δ_{e}), τ_{*}^{'} (Δ_{e}) ⟩$ is well defined where $τ$ and $τ^{'}$ are correspondences. The paper ends with a brief discussion of heights and $L$ -functions in the case that $X$ is a modular curve.

The Mordell conjecture revisited

Enrico Bombieri (1990)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The number of curves of genus two with elliptic differentials.

Ernst Kani (1997)

Journal für die reine und angewandte Mathematik

The $p$ -part of Tate-Shafarevich groups of elliptic curves can be arbitrarily large

Remke Kloosterman (2005)

Journal de Théorie des Nombres de Bordeaux

In this paper we show that for every prime $p \geq 5$ the dimension of the $p$ -torsion in the Tate-Shafarevich group of $E / K$ can be arbitrarily large, where $E$ is an elliptic curve defined over a number field $K$ , with $[K : ℚ]$ bounded by a constant depending only on $p$ . From this we deduce that the dimension of the $p$ -torsion in the Tate-Shafarevich group of $A / ℚ$ can be arbitrarily large, where $A$ is an abelian variety, with $dim A$ bounded by a constant depending only on $p$ .

The p-Primary Component of the Cuspidal Divisor Class Group on the Modular Curve X(p).

Serge Lang, Daniel S. Kubert (1978)

Mathematische Annalen

The Schottky-Jung theorem for Mumford curves

Guido Van Steen (1989)

Annales de l'institut Fourier

The Schottky-Jung proportionality theorem, from which the Schottky relation for theta functions follows, is proved for Mumford curves, i.e. curves defined over a non-archimedean valued field which are parameterized by a Schottky group.