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University of Cambridge > Talks.cam > Algebraic Geometry Seminar > Comparing obstructions to local-global principles for rational points over semiglobal fields

## Comparing obstructions to local-global principles for rational points over semiglobal fieldsAdd to your list(s) Download to your calendar using vCal - Valentijn Karemaker, Utrecht University
- Wednesday 27 November 2019, 14:15-15:15
- CMS MR13.
If you have a question about this talk, please contact Dhruv Ranganathan. 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 This talk is part of the Algebraic Geometry Seminar series. ## This talk is included in these lists:- Algebraic Geometry Seminar
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