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SUMMARY:Rachel Newton
DTSTART:20201007T150000Z
DTEND:20201007T160000Z
DTSTAMP:20260418T064345Z
UID:LNTS/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/13/">Ev
 aluating the wild Brauer group</a>\nby Rachel Newton as part of London num
 ber theory seminar\n\n\nAbstract\nThe local-global approach to the study o
 f rational points on varieties over number fields begins by embedding the 
 set of rational points on a variety X into the set of its adelic points. T
 he Brauer-Manin pairing cuts out a subset of the adelic points\, called th
 e Brauer-Manin set\, that contains the rational points. If the set of adel
 ic points is non-empty but the Brauer-Manin set is empty then we say there
 's a Brauer-Manin obstruction to the existence of rational points on X. Co
 mputing the Brauer-Manin pairing involves evaluating elements of the Braue
 r group of X at local points. If an element of the Brauer group has order 
 coprime to p\, then its evaluation at a p-adic point factors via reduction
  of the point modulo p. For p-torsion elements this is no longer the case:
  in order to compute the evaluation map one must know the point to a highe
 r p-adic precision. Classifying p-torsion Brauer group elements according 
 to the precision required to evaluate them at p-adic points gives a filtra
 tion which we describe using work of Bloch and Kato. Applications of our w
 ork include addressing Swinnerton-Dyer's question about which places can p
 lay a role in the Brauer-Manin obstruction. This is joint work with Martin
  Bright.\n
LOCATION:https://researchseminars.org/talk/LNTS/13/
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