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The 2-Primary Class Group of Certain Hyperelliptic Curves

✍ Scribed by Gunther Cornelissen

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 167 KB
Volume: 91
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2680

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✦ Synopsis

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 y 2 =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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