Abstract: (0.1) Question Given an abelian variety A; does there exist an algebraic curve C such that
there is an isogeny between A and the Jacobian of C ?
• If the dimension of A is at most three, such a curve exists; see (1.3).
• For any g ≥ 4 there exists an abelian variety A of dim(A) = g over C such that there
is no algebraic curve C which admits an isogeny A ∼ Jac(A), see (3.1). One of the
arguments which proves this fact (uncountability of the ground field) does not hold over
a countable field.
Publication Year: 2005
Publication Date: 2005-01-01
Language: en
Type: article
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Cited By Count: 5
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