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SUMMARY:Carlos Castano-Bernard
DTSTART:20260422T160000Z
DTEND:20260422T170000Z
DTSTAMP:20260422T101948Z
UID:FGC-IPM/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGC-IPM/68/"
 >The Atkin-Lehner-Li group of Shimura's modular curve</a>\nby Carlos Casta
 no-Bernard as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nLe
 t X_\\chi(N) be the double covering of X_0(N) associated to \\chi.\nWe sho
 w that the group W_\\chi$ generated by the Atkin-Lehner-Li\nautomorphisms 
 w_Q of X_\\chi(N) is a central extension of an\nelementary abelian 2-group
 . We also characterise when w_Q lies\nin the centre Z(W_\\chi) of W_\\chi 
 in terms of genus theory.\nFinally\, we decompose W_\\chi as a product of 
 an elementary\nabelian 2-group with either an extra-special 2-group\, the 
 Pauli group\,\nor C_4\, if the extension is non-trivial.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/68/
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