IPM Calendar 
Sunday 24 January 2021   Today  
Events for day: Wednesday 18 September 2019    
           15:00 - 17:00     Lecture
Model Theory of Adeles: Recent Developments


This is joint work with Angus Macintyre. I'll discuss the following topics:
1) Solution to a question of Ax (1968) asking whether the the theory of all the rings Z/mZ is ]decidable for all m>1. (Ax proved the special case when m runs through all the primes in his celebrated work on pseudo-finite fields).
2) An old question asking to what extent the adele ring of a number field determines the number field. It is known that it does not determine it in general up to isomorphism. We show that elementary equivalence of adele rings implies isomorphism.
3) An axiomatization of the theory of the adeles.
4) Connections ...