Arithmetic, Geometry and Coding Theory

Yves Aubry (1, 2) , Gilles Lachaud (2)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 IML - Institut de mathématiques de Luminy

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

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Yves Aubry, Gilles Lachaud. Arithmetic, Geometry and Coding Theory. Société Mathématique de France. Société Mathématique de France, pp.216, 2005, Séminaires et congrès, 2-85629-175-9. ⟨hal-00979006⟩