Maximal abelian extension of X(p) unramified outside cusps

Takao Yamazaki, Yifan Yang

Research output: Contribution to journalArticlepeer-review

Abstract

Let p be a prime number. Mazur proved that a geometrically maximal unramified abelian covering of X(p) over Q is given by the Shimura covering X2(p) → X(p) , that is, a unique subcovering of X1(p) → X(p) of degree Np: = (p- 1) / gcd (p- 1 , 12). In this short paper, we show that a geometrically maximal abelian covering X2′(p)→X0(p) of X(p) over Q unramified outside cusps is cyclic of degree 2 Np. The main ingredient for the construction of X2′(p) is the generalized Dedekind eta functions.

Original languageEnglish
Pages (from-to)441-455
Number of pages15
Journalmanuscripta mathematica
Volume162
Issue number3-4
DOIs
Publication statusPublished - 2020 Jul 1

ASJC Scopus subject areas

  • Mathematics(all)

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