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Let K be a complete discretely valued field, let F be the function field of a
curve over K, and let Z be a variety over F. When the existence of rational
points on Z over a set of local field extensions of F implies the existence of
rational points on Z over F, we say a local-global principle holds for Z.
In this talk, we will compare local-global principles, and obstructions to such
principles, for two choices of local field extensions of F. On the one hand we
consider completions F_v at valuations of F, and on the other hand we consider
fields F_P which are the fraction fields of completed local rings at points on
the special fibre of a regular model of F.
We show that if a local-global principle with respect to valuations holds, then
so does a local-global principle with respect to points, for all models of F.
Conversely, we prove that there exists a suitable model of F such that if a
local-global principle with respect to points holds for this model, then so does
a local-global principle with respect to valuations.
This is joint work with David Harbater, Julia Hartmann, and Florian Pop
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Freitag, den 7. Dezember 2018 um 13:30 Uhr, in INF 205, SR A Freitag, den 7. Dezember 2018 at 13:30, in INF 205, SR A

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Oliver Thomas