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The size of the primes obstructing the existence of rational points and Brownian motion

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Speaker: 
Efthymios Sofos
Affiliation: 
MPIM
Date: 
Tue, 2018-10-02 14:00 - 15:00
Location: 
MPIM Lecture Hall
The sequence of the primes p for which a variety over the rational numbers has no p-adic point plays a fundamental role in arithmetic geometry. 
This sequence is deterministic, however, we prove that if we choose a typical variety from a family then the sequence has random behaviour. 
We furthermore prove that this behaviour is modelled by a random walk in Brownian motion. This has several consequences, one of them being 
the description of the finer properties of the distribution of the primes in this sequence via the Feynman-Kac formula.
 
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