EuDML | Browse

Page 1

Displaying 1 – 5 of 5

Integral canonical models of Shimura varieties

Mark Kisin (2009)

Journal de Théorie des Nombres de Bordeaux

The aim of these notes is to provide an introduction to the subject of integral canonical models of Shimura varieties, and then to sketch a proof of the existence of such models for Shimura varieties of Hodge and, more generally, abelian type. For full details the reader is refered to [Ki 3].

Intersections sur des courbes modulaires.

Loic Merel (1993)

Manuscripta mathematica

Involutory elliptic curves over $𝔽_{q} (T)$

Andreas Schweizer (1998)

Journal de théorie des nombres de Bordeaux

For $n \in 𝔽_{q} [T]$ let $G$ be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve $X_{0} (𝔫)$ . We determine all $𝔫$ and $G$ for which the quotient curve $G ∖ X_{0} (𝔫)$ is rational or elliptic.

Isogeny orbits in a family of abelian varieties

Qian Lin, Ming-Xi Wang (2015)

Acta Arithmetica

We prove that if a curve of a nonisotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety, then it is either torsion or contained in a fiber. This result fits into the context of the Zilber-Pink conjecture. Moreover, by using the polyhedral reduction theory we give a new proof of a result of Bertrand.

Iwasawa modules attached to congruences of cusp forms

Haruzo Hida (1986)

Annales scientifiques de l'École Normale Supérieure