Hyperelliptic curves with maximal Galois action on the torsion points of their Jacobians
نویسندگان
چکیده
منابع مشابه
Elliptic Curves with Maximal Galois Action on Their Torsion Points
Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, ρE : Gal(k/k) → GL2(b Z). For a fixed number field k, we describe the image of ρE for a “random” elliptic curve E over k. In particular, if k 6= Q is linearly disjoint from the cyclotomic extension of Q, then ρE will be surjective for “most” elliptic curves over k.
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We begin with a brief history of the problem of determining the set of points of a curve that map to torsion points of the curve’s Jacobian. Let K be a number field, and suppose that X/K is an algebraic curve of genus g ≥ 2. Assume, furthermore, that X is embedded in its Jacobian variety J via a K-rational Albanese map i; thus there is a K-rational divisor D of degree one on X such that i = iD ...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2020
ISSN: 0022-2518
DOI: 10.1512/iumj.2020.69.8178