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Let X be a proper smooth variety having an affine open subset defined by the normic equation $N_{k (\sqrt a, \sqrt b) / k} (x) = Q (t ₁, . . ., t ₘ) ²$ over a number field k. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of X; (2) the analogue for rational points is also valid assuming Schinzel’s hypothesis.

Manin’s conjecture for a quartic del Pezzo surface with $A_{4}$ singularity

Tim D. Browning, Ulrich Derenthal (2009)

Annales de l’institut Fourier

The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type $A_{4}$ .

Meromorphe Funktionen auf Mumfords Kompaktifizierung der universellen elliptischen Kurve N-ter Stufe.

Rolf Berndt (1981)

Journal für die reine und angewandte Mathematik

Méthodes algébriques et démonstrations de transcendance locales.

Daniel BERTRAND (1974/1975)

Seminaire de Théorie des Nombres de Bordeaux

Minimal resolution and stable reduction of $X_{0} (N)$

Bas Edixhoven (1990)

Annales de l'institut Fourier

Let $N \geq 1$ be an integer. Let $X_{0} (N)$ be the modular curve over $Z$ , as constructed by Katz and Mazur. The minimal resolution of $X_{0} (N)$ over $Z [1 / 6]$ is computed. Let $p \geq 5$ be a prime, such that $N = p^{2} M$ , with $M$ prime to $p$ . Let $n = (p^{2} - 1) / 2$ . It is shown that $X_{0} (N)$ has stable reduction at $p$ over $Q [\sqrt[n]{p}]$ , and the fibre at $p$ of the stable model is computed.

Models of group schemes of roots of unity

A. Mézard, M. Romagny, D. Tossici (2013)

Annales de l’institut Fourier

Let $𝒪_{K}$ be a discrete valuation ring of mixed characteristics $(0, p)$ , with residue field $k$ . Using work of Sekiguchi and Suwa, we construct some finite flat $𝒪_{K}$ -models of the group scheme $μ_{p^{n}, K}$ of $p^{n}$ -th roots of unity, which we call Kummer group schemes. We carefully set out the general framework and algebraic properties of this construction. When $k$ is perfect and $𝒪_{K}$ is a complete totally ramified extension of the ring of Witt vectors $W (k)$ , we provide a parallel study of the Breuil-Kisin modules of finite flat models...

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Displaying 101 – 120 of 271

Iwasawa L-Functions of Varieties over Algebraic Number Fields.

Konstruktion von Zahl- und Funktionenkörpern mit vorgegebener Galoisgruppe.

Kubert-lang units and elliptic curves without complex multiplication

La conjecture de Mordell

La conjecture de Mordell pour les corps de fonctions

La conjecture de Weil pour les surfaces K3.

Lang’s conjecture in characteristic $p$ : an explicit bound

Le groupe cuspidal des courbes de Fermat

Le spectre résiduel de $GL (n)$

Le théorème des zéros pour les variétés analytiques réelles de dimension $2$

Les constantes des équations fonctionnelles

Local-global principle for certain biquadratic normic bundles

Manin’s conjecture for a quartic del Pezzo surface with $A_{4}$ singularity

Meromorphe Funktionen auf Mumfords Kompaktifizierung der universellen elliptischen Kurve N-ter Stufe.

Méthodes algébriques et démonstrations de transcendance locales.

Minimal resolution and stable reduction of $X_{0} (N)$

Models of group schemes of roots of unity

Modular Curves and the Class Group of Q(...p).

Modulare Einheiten für Funktionenkörper.

ndependence of Modular Units on Tate Curves.

Currently displaying 101 – 120 of 271