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SUMMARY:Local systems on curves over finite fields and boundedness of trac
 e fields
DTSTART:20221026T141500
DTEND:20221026T160000
DTSTAMP:20260916T003223Z
UID:1bb527fb282546ebc920f62a880baa2f371b427dd577c3b614e74cd1
CATEGORIES:Conferences - Seminars
DESCRIPTION:Josh Lam (Humboldt University\, Berlin)\nFor a local system on
  a curve over a finite field\, the work of Lafforgue shows that there is a
  well defined number field\, referred to as the trace field\, generated by
  the traces of Frobenius elements at the closed points. A basic question i
 s how do such trace fields vary as the curve and the local system vary. Ba
 sed on computations of Kontsevich\, as well as Maeda's conjecture in the 
 number field setting\, one expects that generically such fields are as lar
 ge as they are allowed to be. I will show that\, in the case of rank two l
 ocal systems\, as we vary over all pointed curves of type (g\,n) over all 
 finite fields\, the set of trace fields of fixed degree is finite. This ca
 n be viewed as a uniform (across the moduli of curves) version of a finite
 ness result of Deligne's in positive characteristic.
LOCATION:GR A3 31 https://plan.epfl.ch/?room==GR%20A3%2031
STATUS:CONFIRMED
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