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SUMMARY:Part II.  Rigid meromorphic cocycles for orthogonal groups. (Joint
  with Lennart Gehrmann and Mike Lipnowski.)
DTSTART:20220310T150000
DTEND:20220310T154500
DTSTAMP:20261002T022042Z
UID:ab6769d657fbf4f1050cb5e7a3a6cff8e1ad6e01a374a432f924bacb
CATEGORIES:Conferences - Seminars
DESCRIPTION:Henri Darmon (McGill\, Montreal)\nThe rigid meromorphic cocycl
 es of Part I are cocycles on  $PSL(2\,Z[1/p])$\, which is contained in th
 e orthogonal group of a ternary quadratic space of signature $(2\,1)$\, th
 e space of binary quadratic forms with the discriminant form. The notion o
 f rigid meromorphic cocycles can be extended  to  orthogonal groups of a
 rbitrary real signature $(r\,s)$.  The resulting objects can be evaluated
  at ``special points” associated to  tori in the orthogonal group\, and
  these values  lead to non-trivial class invariants in abelian extensions
  of the associated reflex fields. Whereas the real quadratic field case  
 arising from quadratic spaces of signature $(2\,1)$  is now supported by 
 substantial theoretical evidence\, the setting of higher rank orthogonal g
 roups is   more mysterious\, and the evidence for it\, fragmentary and la
 rgely experimental.
LOCATION:CM 0 9 https://plan.epfl.ch/?room==CM%200%209
STATUS:CONFIRMED
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