The 2-primary class group of certain hyperelliptic curves

Gunther Cornelissen

doi:10.1006/jnth.2001.2680

The 2-primary class group of certain hyperelliptic curves

Gunther Cornelissen^*

^*Corresponding author for this work

Sub Fundamental Mathematics

extern

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

Abstract

Let q be an odd prime, e a non-square in the finite field F_q with q elements, p(T) an irreducible polynomial in F_q[T] and A the affine coordinate ring of the hyperelliptic curve y² = ep(T) in the (y, T)-plane. We use class field theory to study the dependence on deg(p) of the divisibility by 2, 4, and 8 of the class number of the Dedekind ring A. Applications to Jacobians and type numbers of certain quaternion algebras are given.

Original language	English
Pages (from-to)	174-185
Number of pages	12
Journal	Journal of Number Theory
Volume	91
Issue number	1
DOIs	https://doi.org/10.1006/jnth.2001.2680
Publication status	Published - Nov 2001

Bibliographical note

Funding Information:
The author is post-d octoral fellow of the Fund for Scientific Research - Fland ers (FWO - Vlaanderen). This work was done while visiting the MPIM.

Funding

The author is post-d octoral fellow of the Fund for Scientific Research - Fland ers (FWO - Vlaanderen). This work was done while visiting the MPIM.

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10.1006/jnth.2001.2680

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title = "The 2-primary class group of certain hyperelliptic curves",

abstract = "Let q be an odd prime, e a non-square in the finite field Fq with q elements, p(T) an irreducible polynomial in Fq[T] and A the affine coordinate ring of the hyperelliptic curve y2 = ep(T) in the (y, T)-plane. We use class field theory to study the dependence on deg(p) of the divisibility by 2, 4, and 8 of the class number of the Dedekind ring A. Applications to Jacobians and type numbers of certain quaternion algebras are given.",

author = "Gunther Cornelissen",

note = "Funding Information: The author is post-d octoral fellow of the Fund for Scientific Research - Fland ers (FWO - Vlaanderen). This work was done while visiting the MPIM.",

year = "2001",

month = nov,

doi = "10.1006/jnth.2001.2680",

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N2 - Let q be an odd prime, e a non-square in the finite field Fq with q elements, p(T) an irreducible polynomial in Fq[T] and A the affine coordinate ring of the hyperelliptic curve y2 = ep(T) in the (y, T)-plane. We use class field theory to study the dependence on deg(p) of the divisibility by 2, 4, and 8 of the class number of the Dedekind ring A. Applications to Jacobians and type numbers of certain quaternion algebras are given.

AB - Let q be an odd prime, e a non-square in the finite field Fq with q elements, p(T) an irreducible polynomial in Fq[T] and A the affine coordinate ring of the hyperelliptic curve y2 = ep(T) in the (y, T)-plane. We use class field theory to study the dependence on deg(p) of the divisibility by 2, 4, and 8 of the class number of the Dedekind ring A. Applications to Jacobians and type numbers of certain quaternion algebras are given.

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DO - 10.1006/jnth.2001.2680

M3 - Article

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VL - 91

SP - 174

EP - 185

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

The 2-primary class group of certain hyperelliptic curves

Abstract

Bibliographical note

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