BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Comparing obstructions to local-global principles
for rational points over semiglobal fields - Valen
tijn Karemaker\, Utrecht University
DTSTART;TZID=Europe/London:20191127T141500
DTEND;TZID=Europe/London:20191127T151500
UID:TALK129859AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/129859
DESCRIPTION:Let K be a complete discretely valued field\, let
F be the function field of a curve over K\, and le
t Z be a variety over F. When the existence of rat
ional points on Z over a set of local field extens
ions of F implies the existence of rational points
on Z over F\, we say a local-global principle hol
ds for Z.\n\nIn this talk\, we will compare local-
global principles\, and obstructions to such princ
iples\, 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 cons
ider fields F_P which are the fraction fields of c
ompleted local rings at points on the special fibr
e of a regular model of F.\n\nWe show that if a lo
cal-global principle with respect to valuations ho
lds\, then so does a local-global principle with r
espect 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 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\, Juli
a Hartmann\, and Florian Pop
LOCATION:CMS MR13
CONTACT:Dhruv Ranganathan
END:VEVENT
END:VCALENDAR