A model theory for adeles and connections to number theory

A model theory for adeles and connections to number theory

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Jamshid Derakhshan, Oxford University
Fine Hall 314

This is joint work with Angus Macintyre. Using p-adic model theory and other tools, we develop a model theory for the adeles of a number field. I will state some of the main results, and discuss some recent emerging connections to Serre's work on the number of solutions modulo p of a variety, to analytic properties of zeta and L-functions, and to adelic Poisson summation formulas.