Maximal abelian extension of X(p) unramified outside cusps

Takao Yamazaki; Yifan Yang

doi:10.1007/s00229-019-01136-7

Maximal abelian extension of X(p) unramified outside cusps

Takao Yamazaki, Yifan Yang

SCI - Mathematics

Research output: Contribution to journal › Article

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 N_p: = (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 N_p. The main ingredient for the construction of X2′(p) is the generalized Dedekind eta functions.

Original language	English
Journal	manuscripta mathematica
DOIs	https://doi.org/10.1007/s00229-019-01136-7
Publication status	Published - 2019 Jan 1

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s00229-019-01136-7

Fingerprint Dive into the research topics of 'Maximal abelian extension of X(p) unramified outside cusps'. Together they form a unique fingerprint.

Cite this

Yamazaki, T., & Yang, Y. (2019). Maximal abelian extension of X(p) unramified outside cusps. manuscripta mathematica. https://doi.org/10.1007/s00229-019-01136-7

@article{04f3f12a17604ab18deaf69d10ecd8e8,

title = "Maximal abelian extension of X(p) unramified outside cusps",

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.",

author = "Takao Yamazaki and Yifan Yang",

year = "2019",

month = jan,

day = "1",

doi = "10.1007/s00229-019-01136-7",

language = "English",

journal = "Manuscripta Mathematica",

issn = "0025-2611",

publisher = "Springer New York",

}

TY - JOUR

T1 - Maximal abelian extension of X(p) unramified outside cusps

AU - Yamazaki, Takao

AU - Yang, Yifan

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85069725943&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069725943&partnerID=8YFLogxK

U2 - 10.1007/s00229-019-01136-7

DO - 10.1007/s00229-019-01136-7

M3 - Article

AN - SCOPUS:85069725943

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

ER -