Arithmetic, Geometry and Coding Theory
Résumé
In may 2003, two events have been held in the ''Centre International de Rencontres Mathématiques'' in Marseille (France), devoted to Arithmetic, Geometry and their applications in Coding theory and Cryptography: an European school ''Algebraic Geometry and Information Theory'' and the 9-th international conference ''Arithmetic, Geometry and Coding Theory''. Some of the courses and the conferences are published in this volume. The topics were theoretical for some ones and turned towards applications for others: abelian varieties, function fields and curves over finite fields, Galois group of pro-p-extensions, Dedekind zeta functions of number fields, numerical semigroups, Waring numbers, bilinear complexity of the multiplication in finite fields and class number problems.
Mots clés
hyperelliptic curves
p-adic representations
class field towers
Galois groups
rational points
continued fractions
regulators
ideal class number
bilinear complexity
hyperelliptic jacobians
Zeta functions
abelian varieties
functions fields
curves over finite fields
towers of function fields
finite fields
graphs
numerical semigroups
polynomials over finite fields
cryptography