p-adic Dynamics of Hecke Operators on Modular Curves

Eyal Z Goran, Payman L Kassaei

Research output: Working paper/PreprintPreprint

Abstract

In this paper we study the p-adic dynamics of prime-to-p Hecke operators on the set of points of modular curves in both cases of good ordinary and supersingular reduction. We pay special attention to the dynamics on the set of singular moduli. In the case of ordinary reduction we employ the Serre-Tate coordinates, while in the supersingular case we use a parameter on the deformation space of the unique formal group of height 2 over F¯¯¯p, and take advantage of the Gross-Hopkins period map.
Original languageEnglish
PublisherarXiv
Publication statusE-pub ahead of print - 20 Oct 2019

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