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Models of some genus one curves with applications to descent

✍ Scribed by Catherine O’Neil

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
266 KB
Volume
112
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let p denote a prime, and K a field of characteristic prime to p and containing the pth roots of unity. For p equal to 3 and 5, the author finds a scheme T p and a family of genus one curves over T p such that any genus one curve defined over the field K of index p whose Jacobian elliptic curve E has Ep = Ep is isomorphic to a curve lying over a Kpoint of T p . The author then relates the explicit presentation of such families to the program of descent on elliptic curves.

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