WORKSHOP 2
Density Problems in Arithmetics
3-7 April 2023
Place: CIRM (Marseille Luminy, France)

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PRE REGISTRATIONS (Available letters)

INVITATION / VISA LETTER

PARTICIPANTS

SCHEDULE & ABSTRACTS

PRACTICAL INFO

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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.

SCIENTIFIC COMMITTEE

• Chantal David (Concordia University),
• Ronald van Luijk (Leiden University),
  
• Francesco Pappalardi (Università Roma Tre),
• Antonella Perucca (Université du Luxembourg)

ORGANIZING COMMITTEE

• Samuele Anni (Aix-Marseille Université),
  
• Peter Stevenhagen (Leiden University)
• Alex Bartel (University of Glasgow)
• Rachel Newton (University of Reading)

SPEAKERS (list to be completed)

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