Article

Mathematische Zeitschrift

, Volume 273, Issue 3, pp 1139-1159

First online:

Action of Hecke operators on cohomology of modular curves of level two

  • Naoki ImaiAffiliated withResearch Institute for Mathematical Sciences, Kyoto University Email author 
  • , Takahiro TsushimaAffiliated withFaculty of Mathematics, Kyushu University

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Abstract

We calculate the action of the p-th Hecke operator and the inertia group on the -adic cohomology of modular curve of level Γ0(p 2) under the assumption p ≥ 13, using only a local geometrical method. We also calculate the action of the p-th Hecke operator and the inertia group on the -adic cohomology of the Lubin-Tate space of the same level over the maximal unramified extension of \({\mathbb{Q}_p}\).

Mathematics Subject Classification (2010)

Primary 11G18 Secondary 14G35