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SUMMARY:Comparing obstructions to local-global principles for rational poi
 nts over semiglobal fields - Valentijn Karemaker\, Utrecht University
DTSTART:20191127T141500Z
DTEND:20191127T151500Z
UID:TALK129859@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Let K be a complete discretely valued field\, let F be the fun
 ction field of a curve over K\, and let Z be a variety over F. When the ex
 istence 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-glob
 al principle holds for Z.\n\nIn this talk\, we will compare local-global p
 rinciples\, and obstructions to such principles\, for two choices of local
  field extensions of F. On the one hand we consider completions F_v at val
 uations 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.\n\nWe show that if a local-global principle with re
 spect to valuations holds\, then so does a local-global principle with res
 pect to points\, for all models of F. Conversely\, we prove that there exi
 sts a suitable model of F such that if a local-global principle with respe
 ct to points holds for this model\, then so does a local-global principle 
 with respect to valuations.\n\nThis is joint work with David Harbater\, Ju
 lia Hartmann\, and Florian Pop
LOCATION:CMS MR13
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