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Obstructions au principe de Hasse et à l’approximation faible

Emmanuel Peyre (2003/2004)

Séminaire Bourbaki

Si un système d’équations polynomiales à coefficients entiers admet une solution dans $𝐐^{n}$ , il en admet sur tout complété $p$ -adique ou réel de $𝐐$ . La réciproque a été démontrée par Hasse pour les quadriques, mais elle est fausse en général. Une grande partie des contre-exemples connus peuvent être expliqués à l’aide de l’obstruction de Brauer-Manin, basée sur la théorie du corps de classe. Il est donc naturel de se demander si, pour certaines classes de variétés, cette obstruction est la seule. Le but...

On algebraic tori of norm type.

W. Hürlimann (1984)

Commentarii mathematici Helvetici

On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem

Umberto Zannier (1995)

Acta Arithmetica

On diagonal cubic surfaces.

Andrew Bremner (1988)

Manuscripta mathematica

On galois automorphisms of the fundamental group of the projective line minus three points.

Hiroaki Nakamura (1991)

Mathematische Zeitschrift

On K1 of curves over global fields.

Wayne Raskin (1990)

Mathematische Annalen

On Manin's conditional algorithm

Horst G. Zimmer (1977)

Mémoires de la Société Mathématique de France

On Manin's conjecture for a certain singular cubic surface

Régis de La Bretèche, Tim D. Browning, Ulrich Derenthal (2007)

Annales scientifiques de l'École Normale Supérieure

On nonary cubic forms.

Christopher Hooley (1988)

Journal für die reine und angewandte Mathematik

On $p$ -adic analytic families of Galois representations

B. Mazur, A. Wiles (1986)

Compositio Mathematica

On rational torsion points of central $ℚ$ -curves

Fumio Sairaiji, Takuya Yamauchi (2008)

Journal de Théorie des Nombres de Bordeaux

Let $E$ be a central $ℚ$ -curve over a polyquadratic field $k$ . In this article we give an upper bound for prime divisors of the order of the $k$ -rational torsion subgroup $E_{t o r s} (k)$ (see Theorems 1.1 and 1.2). The notion of central $ℚ$ -curves is a generalization of that of elliptic curves over $ℚ$ . Our result is a generalization of Theorem 2 of Mazur [12], and it is a precision of the upper bounds of Merel [15] and Oesterlé [17].

Currently displaying 1 – 20 of 32

Page 1 Next

Displaying 1 – 20 of 32

Obstructions au principe de Hasse et à l’approximation faible

On algebraic tori of norm type.

On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem

On diagonal cubic surfaces.

On galois automorphisms of the fundamental group of the projective line minus three points.

On K1 of curves over global fields.

On Manin's conditional algorithm

On Manin's conjecture for a certain singular cubic surface

On nonary cubic forms.

On $p$ -adic analytic families of Galois representations

On rational torsion points of central $ℚ$ -curves

On square values of quadratics

On squares of squares II

On the arithmetic of an elliptic curve over a $Z_{p}$ -extension

On the Arithmetic of Special Values of L Functions.

On the behavior of Igusa,'s local zeta function in towers of field extension

On the Conjecture of Birch and Swinnerton-Dyer

On the Construction of Galois Extensions of Function Fields and Number Fields.

On the de Rham isomorphism for Drinfeld modules.

On the Diophantine equation ... (X, Y) = ... (x, y).

Currently displaying 1 – 20 of 32