Seminar: Carlos Castano-Bernard - The Atkin-Lehner-Li group of Shimura's modular curve (Apr 22, 2026)

Çarşamba, 22 Nisan 2026

Speaker: Carlos Castano-Bernard (Universidad de Colima)

Title: The Atkin-Lehner-Li group of Shimura's modular curve

Time: April 22, Wednesday, 2026 at 19:00 (Istanbul LT)

Place: Online

Meeting ID: 997 1547 1656
Passcode: 848084

Abstract: Let ( X_\chi(N) ) be the double covering of ( X_0(N) ) associated to ( \chi ). We show that the group ( W_\chi ) generated by the Atkin-Lehner-Li automorphisms ( w_Q ) of ( X_\chi(N) ) is a central extension of an elementary abelian 2-group. We also characterise when ( w_Q ) lies in the centre ( Z(W_\chi) ) of ( W_\chi ) in terms of genus theory. Finally, we decompose ( W_\chi ) as a product of an elementary abelian 2-group with either an extra-special 2-group, the Pauli group, or ( C_4 ), if the extension is non-trivial.