An example of Brauer-Manin obstruction to weak approximation at a prime with good reduction

Abstract: A way to study rational points on a variety is by looking at their image in the $p$-adic points. Some natural questions that arise are the following: is there any obstruction to weak approximation on the variety? Which primes might be involved in it? Bright and Newton have proven that for K3 surfaces defined over number fields primes with good ordinary reduction play a role in the Brauer--Manin obstruction to weak approximation.

In this talk I will give an explicit example of this phenomenon. In particular, I will exhibit a K3 surface defined over the rational numbers having good reduction at $2$, and for which $2$ is a prime at which weak approximation is obstructed.

algebraic geometrycombinatoricsdynamical systemsgeneral topologynumber theory

Audience: researchers in the topic

ZORP (zoom on rational points)

Series comments: 2 talks on a Friday, roughly once per month.

Online coffee break in between.