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

Page 1 Next

Displaying 1 – 20 of 134

Showing per page

Tamely ramified Hida theory

Assaf Goldberger, Ehud de Shalit (2002)

Annales de l’institut Fourier

Let J 1 be the Jacobian of the modular curve associated with Γ 1 ( N p ) , ( p , N ) = 1 and J 0 the one associated with Γ 1 ( N ) ∩ Γ 0 ( p ) . We study J 1 [ p - 1 ] as a Hecke and Galois-module. We relate a certain matrix of p -adic periods to the infinitesimal deformation of the U p -operator.

The Analytic Rank of a Family of Jacobians of Fermat Curves

Tomasz Jędrzejak (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

We study the family of curves F m ( p ) : x p + y p = m , where p is an odd prime and m is a pth power free integer. We prove some results about the distribution of root numbers of the L-functions of the hyperelliptic curves associated to the curves F m ( p ) . As a corollary we conclude that the jacobians of the curves F m ( 5 ) with even analytic rank and those with odd analytic rank are equally distributed.

The arithmetic of certain del Pezzo surfaces and K3 surfaces

Dong Quan Ngoc Nguyen (2012)

Journal de Théorie des Nombres de Bordeaux

We construct del Pezzo surfaces of degree 4 violating the Hasse principle explained by the Brauer-Manin obstruction. Using these del Pezzo surfaces, we show that there are algebraic families of K 3 surfaces violating the Hasse principle explained by the Brauer-Manin obstruction. Various examples are given.

The arithmetic of curves defined by iteration

Wade Hindes (2015)

Acta Arithmetica

We show how the size of the Galois groups of iterates of a quadratic polynomial f can be parametrized by certain rational points on the curves Cₙ: y² = fⁿ(x) and their quadratic twists (here fⁿ denotes the nth iterate of f). To that end, we study the arithmetic of such curves over global and finite fields, translating key problems in the arithmetic of polynomial iteration into a geometric framework. This point of view has several dynamical applications. For instance, we establish a maximality theorem...

The Bloch-Kato conjecture on special values of L -functions. A survey of known results

Guido Kings (2003)

Journal de théorie des nombres de Bordeaux

This paper contains an overview of the known cases of the Bloch-Kato conjecture. It does not attempt to overview the known cases of the Beilinson conjecture and also excludes the Birch and Swinnerton-Dyer point. The paper starts with a brief review of the formulation of the general conjecture. The final part gives a brief sketch of the proofs in the known cases.

Currently displaying 1 – 20 of 134

Page 1 Next