Abelian surfaces of GL₂-type as Jacobians of curves
Abelian surfaces over finite fields as Jacobians. With an appendix by Everett W. Howe.
Abelian varieties, ...-adic representations, and ...-independence.
Abelian varieties and Galois module structure in global function fields.
Abelian varieties over fields of finite characteristic
The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.
Abelian varieties over finite fields with a specified characteristic polynomial modulo
We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial modulo . As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order .
Abelian varieties-Galois representation and properties of ordinary reduction
Abstract class field theory (formatting of modules).
Adelic equidistribution of tori and equidistribution of CM points. (Équidistribution adélique des tores et équidistribution des points CM.)
Algebraic covers : field of moduli versus field of definition
Algebraic leaves of algebraic foliations over number fields
We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields. Namely, consider a number field embedded in , a smooth algebraic variety over , equipped with a rational point , and an algebraic subbundle of the its tangent bundle , defined over . Assume moreover that the vector bundle is involutive, i.e., closed under Lie bracket. Then it defines an holomorphic foliation of the analytic manifold , and one may consider its leaf through . We prove...
Algebraic points of low degree on the Fermat quintic
Algebraic S-integers of fixed degree and bounded height
Let k be a number field and S a finite set of places of k containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of S-integers of k. Moreover, we give an asymptotic formula for the number of S̅-integers of bounded height and fixed degree over k, where S̅ is the set of places of k̅ lying above the ones in S.
Algebraic values of G-functions.
Almost -representation. (Presque -représentations.)
Almost powers in the Lucas sequence
The famous problem of determining all perfect powers in the Fibonacci sequence and in the Lucas sequence has recently been resolved [10]. The proofs of those results combine modular techniques from Wiles’ proof of Fermat’s Last Theorem with classical techniques from Baker’s theory and Diophantine approximation. In this paper, we solve the Diophantine equations , with and , for all primes and indeed for all but primes . Here the strategy of [10] is not sufficient due to the sizes of...
Almost primality of group orders of elliptic curves defined over small finite fields.
Amélioration d'une congruence pour certains éléments de Stickelberger quadratiques
An theorem over function fields and applications
We provide a lower bound for the number of distinct zeros of a sum for two rational functions , in term of the degree of , which is sharp whenever have few distinct zeros and poles compared to their degree. This sharpens the “-theorem” of Brownawell-Masser and Voloch in some cases which are sufficient to obtain new finiteness results on diophantine equations over function fields. For instance, we show that the Fermat-type surface contains only finitely many rational or elliptic curves,...
An alternative description of the Drinfeld -adic half-plane
We show that the Deligne formal model of the Drinfeld -adic half-plane relative to a local field represents a moduli problem of polarized -modules with an action of the ring of integers in a quadratic extension of . The proof proceeds by establishing a comparison isomorphism with the Drinfeld moduli problem. This isomorphism reflects the accidental isomorphism of and for a two-dimensional split hermitian space for .