Reflection theorem for divisor class groups of relative quadratic function fields

Yoonjin Lee

doi:10.1016/j.jnt.2007.08.013

Reflection theorem for divisor class groups of relative quadratic function fields

Yoonjin Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We present the reflection theorem for divisor class groups of relative quadratic function fields. Let K be a global function field with constant field F_q. Let L₁ be a quadratic geometric extension of K and let L₂ be its twist by the quadratic constant field extension of K. We show that for every odd integer m that divides q + 1 the divisor class groups of L₁ and L₂ have the same m-rank.

Original language	English
Pages (from-to)	2127-2137
Number of pages	11
Journal	Journal of Number Theory
Volume	128
Issue number	7
DOIs	https://doi.org/10.1016/j.jnt.2007.08.013
State	Published - Jul 2008

Bibliographical note

Funding Information:
* Fax: +82 2 3277 2289. E-mail address: [email protected]. 1 The author was supported by NSERC.

Keywords

Divisor class group
Ideal class group
Quadratic function field
Rank of divisor class group
Reflection theorem

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10.1016/j.jnt.2007.08.013

Cite this

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title = "Reflection theorem for divisor class groups of relative quadratic function fields",

abstract = "We present the reflection theorem for divisor class groups of relative quadratic function fields. Let K be a global function field with constant field Fq. Let L1 be a quadratic geometric extension of K and let L2 be its twist by the quadratic constant field extension of K. We show that for every odd integer m that divides q + 1 the divisor class groups of L1 and L2 have the same m-rank.",

keywords = "Divisor class group, Ideal class group, Quadratic function field, Rank of divisor class group, Reflection theorem",

author = "Yoonjin Lee",

note = "Funding Information: * Fax: +82 2 3277 2289. E-mail address: [email protected]. 1 The author was supported by NSERC.",

year = "2008",

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journal = "Journal of Number Theory",

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PY - 2008/7

Y1 - 2008/7

N2 - We present the reflection theorem for divisor class groups of relative quadratic function fields. Let K be a global function field with constant field Fq. Let L1 be a quadratic geometric extension of K and let L2 be its twist by the quadratic constant field extension of K. We show that for every odd integer m that divides q + 1 the divisor class groups of L1 and L2 have the same m-rank.

AB - We present the reflection theorem for divisor class groups of relative quadratic function fields. Let K be a global function field with constant field Fq. Let L1 be a quadratic geometric extension of K and let L2 be its twist by the quadratic constant field extension of K. We show that for every odd integer m that divides q + 1 the divisor class groups of L1 and L2 have the same m-rank.

KW - Divisor class group

KW - Ideal class group

KW - Quadratic function field

KW - Rank of divisor class group

KW - Reflection theorem

UR - https://www.scopus.com/pages/publications/44349123009

U2 - 10.1016/j.jnt.2007.08.013

DO - 10.1016/j.jnt.2007.08.013

M3 - Article

AN - SCOPUS:44349123009

SN - 0022-314X

VL - 128

SP - 2127

EP - 2137

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 7

ER -

Reflection theorem for divisor class groups of relative quadratic function fields

Abstract

Bibliographical note

Keywords

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Cite this