BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Claudio Bravo (University of Chile)
DTSTART:20220701T000000Z
DTEND:20220701T010000Z
DTSTAMP:20260423T052923Z
UID:SiN/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/42/">Quo
 tients of the Bruhat-Tits tree function filed analogs of the Hecke congrue
 nce subgroups</a>\nby Claudio Bravo (University of Chile) as part of Symme
 try in Newcastle\n\nLecture held in Lambert Lounge\, US 321.\n\nAbstract\n
 Let C be a smooth\, projective\, and geometrically connected curve defined
  over a finite field F. For each closed point P_infty of C\, let R be the 
 ring of functions that are regular outside P_infty\, and let K be the comp
 letion path P_infty of the function field of C. In order to study group of
  the form GL_2(R)\, Serre describes the quotient graph GL_2(R)\\T\, where 
 T is the Bruhat-Tits tree defined from SL_2(K). In particular\, Serre show
 s that GL_2(R)\\T is the union of a finite graph and a finite number of ra
 y shaped subgraphs\, which are called cusps. It is not hard to see that fi
 nite index subgroups inherit this property.\nIn this exposition we describ
 e the quotient graph H\\T defined from the action on T of the group H cons
 isting of matrices that are upper triangular modulo I\, where I is an idea
 l R. More specifically\, we give an explicit formula for the cusp number H
 \\T. Then By\, using Bass-Serre theory\, we describe the combinatorial str
 ucture of H. These groups play\, in the function field context\, the same 
 role as the Hecke Congruence subgroups of SL_2(Z). Moreover\, not that the
  groups studied by Serre correspond to the case where the ideal I coincide
 s with the ring R.\n
LOCATION:https://researchseminars.org/talk/SiN/42/
END:VEVENT
END:VCALENDAR