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Rank of K 2 of elliptic curves

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    QingZhong Ji & HouRong Qin

Authors
  1. QingZhong Ji
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  2. HouRong Qin
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Corresponding author

Correspondence to QingZhong Ji.

Additional information

This work was supported by National Natural Science Foundation of China (Grant Nos. 10571080, 10871088) Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200802840003) and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No.708044)

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Ji, Q., Qin, H. Rank of K 2 of elliptic curves. Sci. China Ser. A-Math. 52, 2107–2120 (2009). https://doi.org/10.1007/s11425-009-0022-x

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  • DOI: https://doi.org/10.1007/s11425-009-0022-x

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