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SUMMARY:Adèles and the geometry of schemes
DTSTART:20150922T151500
DTEND:20150922T170000
DTSTAMP:20260504T200044Z
UID:63507e20cccd00c1d2337b79614e5957b4ef6c1384b51987636ac72e
CATEGORIES:Conferences - Seminars
DESCRIPTION:Michael Groechenig\, (Imperial College)\nThe ring of adèles p
 lays a fundamental role in number theory. Our current understanding of cla
 ss field theory\, and its far-reaching extension\, the Langlands Programme
 \, would be inconceivable without it. It is a bridge connecting local and 
 global aspects.\nThere is a similar approach to the geometry of varieties.
  In the first part of my talk I will survey how classical results for alge
 braic curves can be obtained adelically. We will use this to observe an an
 alogy between Serre duality and Autoduality of Jacobians. We conclude this
  part by studying Weil’s adelic uniformization for G-bundles on curves.\
 nIn the second part we will discuss a generalisation of Weil’s result ge
 neral varieties and perfect complexes. As a corollary we obtain that Noeth
 erian schemes can be reconstructed from Beilinson’s cosimplicial ring of
  adèles.
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STATUS:CONFIRMED
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