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

Previous Page 2 Next

Displaying 21 – 40 of 62

Showing per page

Explicit bounds for split reductions of simple abelian varieties

Jeffrey D. Achter (2012)

Journal de Théorie des Nombres de Bordeaux

Let X / K be an absolutely simple abelian variety over a number field; we study whether the reductions X 𝔭 tend to be simple, too. We show that if End ( X ) is a definite quaternion algebra, then the reduction X 𝔭 is geometrically isogenous to the self-product of an absolutely simple abelian variety for 𝔭 in a set of positive density, while if X is of Mumford type, then X 𝔭 is simple for almost all 𝔭 . For a large class of abelian varieties with commutative absolute endomorphism ring, we give an explicit upper bound...

Greatest common divisors of u - 1 , v - 1 in positive characteristic and rational points on curves over finite fields

Pietro Corvaja, Umberto Zannier (2013)

Journal of the European Mathematical Society

In our previous work we proved a bound for the g c d ( u − 1 , v − 1 ) , for S -units u , v of a function field in characteristic zero. This generalized an analogous bound holding over number fields, proved in [3]. As pointed out by Silverman, the exact analogue does not work for function fields in positive characteristic. In the present work, we investigate possible extensions in that direction; it turns out that under suitable assumptions some of the results still hold. For instance we prove Theorems 2 and 3 below, from...

On some equations over finite fields

Ioulia Baoulina (2005)

Journal de Théorie des Nombres de Bordeaux

In this paper, following L. Carlitz we consider some special equations of n variables over the finite field of q elements. We obtain explicit formulas for the number of solutions of these equations, under a certain restriction on n and q .

On the conductor formula of Bloch

Kazuya Kato, Takeshi Saito (2004)

Publications Mathématiques de l'IHÉS

In [6], S. Bloch conjectures a formula for the Artin conductor of the ℓ-adic etale cohomology of a regular model of a variety over a local field and proves it for a curve. The formula, which we call the conductor formula of Bloch, enables us to compute the conductor that measures the wild ramification by using the sheaf of differential 1-forms. In this paper, we prove the formula in arbitrary dimension under the assumption that the reduced closed fiber has normal crossings.

Currently displaying 21 – 40 of 62