Geometric and Analytic Methods for Rational Points

ag.algebraic-geometry nt.number-theory
Start Date
2019-04-15 
End Date
2019-04-19 
Institution
CIRM 
City
Luminy 
Country
France 
Meeting Type
spring school 
Homepage
https://conferences.cirm-math.fr/1989.html 
Contact Name
 

Description

This week is an introductory school to prepare junior participants for the 3-month thematic program "Reinventing rational points" at the Institut Henri Poincaré (April–July 2019). The study of rational points uses a rich mix of methods ranging from algebraic geometry to analytic number theory and has a constantly growing tool kit. The mini-courses will be an introduction to this broad area with an emphasis on new methods and developments. Among the themes to be covered are: Galois cohomology and arithmetic duality theorems; the Brauer group of an algebraic variety; the Brauer-Manin obstruction and descent obstructions to local-to-global principles for rational and integral points, and for zero-cycles; interactions of analytic number theory and geometry, applications of the circle method, sieve methods and additive combinatorics; rational points in families of varieties over local and global fields; new approaches to counting points and varieties. We plan to discuss the state of the art in the research on the Batyrev–Manin principle on the growth of rational points and the Colliot-Thélène conjecture on the Brauer–Manin obstruction, their versions, interrelations and generalisations.

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