TNT 2013-2014

Adelic Number Theory

Instructors: Philippe Michel & Paul Nelson

 

The course is composed of two relatively distinct parts which are run in simultaneously: one concerning the adeles over Q and devoted to arithmetic applications and the other one concerning the adeles over the field of rational fractions over a finite field with application to algebraic curves over finite fields.

Chap 1: Ostrowsky's Theorem

Chap 2: p-adic numbers

Chap 3: The ring of Adeles

Chap 4: Higher dimensional adelic structures.

Chap 5: The ring of Adeles over a number field.

Chap 6: Harmonic analysis on adeles and ideles.

Chap 6: L-functions and Tate's thesis.

Chap 7: Adelic points of groups of matrices: some finiteness results.

 

Références: 

Serre, Jean-Pierre Cours d'arithmétique. (French) Deuxième édition revue et corrigée. Le Mathématicien, No. 2. Presses Universitaires de France, Paris, 1977. 188 pp.

Serre, J.-P. A course in arithmetic. Translated from the French. Graduate Texts in Mathematics, No. 7. Springer-Verlag, New York-Heidelberg, 1973. viii+115 pp.

Ramakrishnan, Dinakar; Valenza, Robert J.Fourier analysis on number fields. (English summary) Graduate Texts in Mathematics, 186. Springer-Verlag, New York, 1999. xxii+350 pp.