The Atkin-Lehner automorphism mod p geometrically
A. Ghitza
Appendix to 'Newforms mod p in squarefree level, with applications to Monsky's Hecke-stable filtration' by S. V. Deo and A. Medvedovsky, Trans. Amer. Math. Soc. Ser. B 6 (2019), 245-273.
We show that the renormalised Atkin-Lehner operator defined in the paper has a natural geometric definition on the Igusa curve covering the modular curve X_0(Nl) mod p.