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Rational points on primary Burniat surfaces

Posted in
Speaker: 
Michael Stoll
Affiliation: 
Bayreuth
Date: 
Wed, 01/04/2015 - 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Primary Burniat surfaces are certain surfaces of general type that
can be constructed as certain covers of a del Pezzo surface of degree 6, but
also as \'etale quotients of a surface contained in the product of three
elliptic curves. Using results by Chevalley-Weil and Faltings, the latter
description implies that rational points on primary Burniat surfaces are not
Zariski dense. We make this statement more concrete by determining the set of
low-genus curves on our surfaces. In favorable cases the set of rational
points can be determined explicitly; we will present some examples.
This is joint work with Ingrid Bauer.

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