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SUMMARY:Rational points\, local-global principles and obstructions
DTSTART;VALUE=DATE-TIME:20151103T133000Z
DTEND;VALUE=DATE-TIME:20151103T143000Z
DTSTAMP;VALUE=DATE-TIME:20190821T133231Z
UID:indico-event-900@indico.math.cnrs.fr
DESCRIPTION:« Return of the IHÉS Postdoc Seminar »\n\n \n\nAbstract: I
n 1970\, Manin observed that the Brauer group Br(X) of a variety X over a
number field K can obstruct the Hasse principle on X. In other words\, the
lack of a K-rational point on X despite the existence of points everywher
e locally is sometimes explained by non-trivial elements in Br(X). Since M
anin's observation\, the Brauer group and the related obstructions have be
en the subject of a great deal of research.\n\nThe 'algebraic' part of the
Brauer group is the part which becomes trivial upon base change to an alg
ebraic closure of K. It is generally easier to handle than the remaining '
transcendental' part and a substantial portion of the literature is devote
d to its study. The transcendental part of the Brauer group is generally m
ore mysterious\, but it is known to have arithmetic importance – it can
obstruct the Hasse principle and weak approximation.\nI will describe rece
nt progress in computing transcendental Brauer groups and obstructions\, a
nd give examples where there is no Brauer-Manin obstruction coming from th
e algebraic part of the Brauer group but a transcendental Brauer class exp
lains why the rational points of a variety fail to be dense in the set of
its adelic points.\n\nhttps://indico.math.cnrs.fr/event/900/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/900/
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