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SUMMARY:Brauer--Manin obstruction and integral points - J.-L. Colliot-Thé
 lène (CNRS and Université Paris-Sud)
DTSTART:20101109T143000Z
DTEND:20101109T153000Z
UID:TALK27107@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:For a scheme over the integers\, the Brauer-Manin set\nconsist
 s of the  integral adèles orthogonal to the Brauer group\nof the variety 
 over the rationals attached to  that  scheme.\nOne then has two  basic que
 stions:  If the Brauer-Manin set  is not empty\,\ndo there exist\nintegral
  points? If so\, are the integral points dense in the Brauer-Manin\nset?\n
 \nFor homogeneous spaces of connected linear algebraic groups\,\nfairly ge
 neral results have been obtained\nXu and the speaker\, Harari\, Xu and Wei
 \, Borovoi and Demarche.\n\nAt least two more cases will be discussed:\n r
 epresentation of an integer as a sum of three cubes (Wittenberg\n and the 
 speaker)\,  integral points on curves (Harari and Voloch).\n
LOCATION:MR13
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