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A lower bound for the canonical height on elliptic curves over abelian extensions

✍ Scribed by Joseph H. Silverman

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
296 KB
Volume
104
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let E=K be an elliptic curve defined over a number field, let Δ₯ be the canonical height on E; and let K ab =K be the maximal abelian extension of K: Extending work of M. Baker (IMRN 29 (2003) 1571-1582), we prove that there is a constant CΓ°E=KÞ40 so that every nontorsion point PAEΓ°K ab Þ satisfies Δ₯Γ°PÞ4CΓ°E=KÞ:

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