Rank of K2 of elliptic curves

We prove that (i) rank( K 2 ( E )) ⩾ 1 for all elliptic curves E defined over ℚ with a rational torsion point of exact order N ⩾ 4; (ii) rank( K 2 ( E )) ⩾ 1 for all but at most one ℝ-isomorphism class of elliptic curves E defined over ℚ with a rational torsion point of exact order 3. We give some s...

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Bibliographic Details
Published inScience in China. Series A, Mathematics, physics, astronomy Vol. 52; no. 10; pp. 2107 - 2120
Main Authors Ji, QingZhong, Qin, HouRong
Format Journal Article
LanguageEnglish
Published Heidelberg SP Science in China Press 01.10.2009
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Néron model
elliptic curve
regulator map
11G05
11G55
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Summary:We prove that (i) rank( K 2 ( E )) ⩾ 1 for all elliptic curves E defined over ℚ with a rational torsion point of exact order N ⩾ 4; (ii) rank( K 2 ( E )) ⩾ 1 for all but at most one ℝ-isomorphism class of elliptic curves E defined over ℚ with a rational torsion point of exact order 3. We give some sufficient conditions for rank( K 2 ( E ℤ )) ⩾ 1.
ISSN:1006-9283
1862-2763
DOI:10.1007/s11425-009-0022-x