WORKSHOP 2
Density problems in Arithmetic
Problèmes de densité en Arithmétique
3-7 April 2023
Place: CIRM (Marseille Luminy, France)
If you are interested in attending, please pre-register following the link below.
All pre-registrations done before February 1st will receive full consideration.
The final list of participants will be decided by the scientific and organizing committees.
DESCRIPTION
ln this workshop, we will consider variants of Artin's primitive root conjecture leading to the study of the Galois groups of various radical extensions. Beyond the case of the multiplicative group studied by Lenstra and others, there are now also interesting results for elliptic radicals, and for division points in more general abelian varieties. ln this context, the elliptic analogue of Artin's conjecture is the Lang-Trotter conjecture, which is still open after more than 40 years.
The Galois representations associated to various division points in abelian varieties are central to understanding the Galois groups of the radical extensions that one tries to explicitly describe in this context, as they control the behaviour of the primes in the underlying problems. Understanding these Galois representations, and the entanglement between the extensions generated by different prime-power radicals, is essential to progress in this area.
ln this circle of problems and questions, one encounters interesting restrictions to local-global principles that will be addressed in this workshop, not only in the context of radical extensions.
SPEAKERS
ORGANIZING COMMITTEE
SCIENTIFIC COMMITTEE