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SUMMARY:On p-primary torsion of the Brauer group in characteristic p
DTSTART:20240227T141500
DTEND:20240227T154500
DTSTAMP:20260924T202723Z
UID:ad6cfa167216245e113efbde789533a055ad531be7065a9f9bfd67b4
CATEGORIES:Conferences - Seminars
DESCRIPTION:Alexei Skorobogatov (Imperial)\nLet k be a finitely generated 
 field. Relation between the Tate conjecture for divisors and finiteness pr
 operties of the Brauer groups of varieties over k is well known\, at least
  for torsion coprime to char(k). Much less is known about p-primary torsio
 n in characteristic p. In a recent paper\, D'Addezio clarified the situati
 on for abelian varieties over fields of positive characteristic. Using sim
 ilar ideas\, I will show that for varieties X and Y satisfying some mild c
 onditions\, the cokernel of the map from Br(X) \\oplus Br(Y) to Br(X\\time
 s Y) is a direct sum of a finite group and a p-group of finite exponent (w
 hich can be infinite). This implies\, for example\, that the transcendenta
 l Brauer group of surfaces dominated by products of curves has finite expo
 nent.
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STATUS:CONFIRMED
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