Displaying 901 – 920 of 1274

Showing per page

Purity of level m stratifications

Marc-Hubert Nicole, Adrian Vasiu, Torsten Wedhorn (2010)

Annales scientifiques de l'École Normale Supérieure

Let k be a field of characteristic p > 0 . Let D m be a BT m over k (i.e., an m -truncated Barsotti–Tate group over k ). Let S be a k -scheme and let X be a BT m over S . Let S D m ( X ) be the subscheme of S which describes the locus where X is locally for the fppf topology isomorphic to D m . If p 5 , we show that S D m ( X ) is pure in S , i.e. the immersion S D m ( X ) S is affine. For p { 2 , 3 } , we prove purity if D m satisfies a certain technical property depending only on its p -torsion D m [ p ] . For p 5 , we apply the developed techniques to show that all level m ...

Quadratic modular symbols on Shimura curves

Pilar Bayer, Iván Blanco-Chacón (2013)

Journal de Théorie des Nombres de Bordeaux

We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic p -adic L -functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach quadratic modular symbols and quadratic p -adic L -functions to more general Shimura curves.

Qualitative properties of coupled parabolic systems of evolution equations

Stefano Cardanobile, Delio Mugnolo (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of sesquilinear mappings. We apply our results to parabolic problems of different nature: a coupled diffusive system arising in neurobiology, a strongly damped wave equation, and a heat equation with dynamic boundary conditions.

Quasi-modular forms attached to elliptic curves, I

Hossein Movasati (2012)

Annales mathématiques Blaise Pascal

In the present text we give a geometric interpretation of quasi-modular forms using moduli of elliptic curves with marked elements in their de Rham cohomologies. In this way differential equations of modular and quasi-modular forms are interpreted as vector fields on such moduli spaces and they can be calculated from the Gauss-Manin connection of the corresponding universal family of elliptic curves. For the full modular group such a differential equation is calculated and it turns out to be the...

R -équivalence sur les familles de variétés rationnelles et méthode de la descente

Alena Pirutka (2012)

Journal de Théorie des Nombres de Bordeaux

La méthode de la descente a été introduite et développée par Colliot-Thélène et Sansuc. Elle permet d’étudier l’arithmétique de certaines variétés rationnelles. Dans ce texte on montre comment il en résulte que pour certaines familles f : X Y de variétés rationnelles sur un corps local k de caractéristique nulle le nombre des classes de R -équivalence de la fibre X y ( k ) est localement constant quand y varie dans Y ( k ) .

Random Thue and Fermat equations

Rainer Dietmann, Oscar Marmon (2015)

Acta Arithmetica

We consider Thue equations of the form a x k + b y k = 1 , and assuming the truth of the abc-conjecture, we show that almost all locally soluble Thue equations of degree at least three violate the Hasse principle. A similar conclusion holds true for Fermat equations a x k + b y k + c z k = 0 of degree at least six.

Rang de courbes elliptiques avec groupe de torsion non trivial

Odile Lecacheux (2003)

Journal de théorie des nombres de Bordeaux

On construit des courbes elliptiques sur ( T ) de rang au moins 3, avec un sous-groupe de torsion non trivial. Par spécialisation, des courbes elliptiques de rang 5 et 6 sur sont obtenues.

Currently displaying 901 – 920 of 1274