Séminaire Stéphanois de Mathématiques Accessibles

Artin's conjecture in Diophantine analysis

by Jörg Brüdern (Göttingen)

C112 (Faculté des sciences de Saint-Etienne)


Faculté des sciences de Saint-Etienne

23 rue du docteur Paul Michelon, Saint-Etienne
In the 1930s, Emil Artin put forward an influential chain of conjectures that concern the existence of p-adic points on projective hypersurfaces. The status of these conjectures is uncertain : in some ways, the conjecture is completely wrong, in others it is almost true. The lecture will formulate Artin's conjectures in elementary terms and then explain their relevance to diophantine analysis. The state of the art will be summarized, with combinatorial methods at the focus of attention.