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.
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