Journal Article

<i>A + B = C</i> and big III's

Benjamin M. M. de Weger

in The Quarterly Journal of Mathematics

Volume 49, issue 1, pages 105-128
Published in print March 1998 | ISSN: 0033-5606
Published online March 1998 | e-ISSN: 1464-3847 | DOI: http://dx.doi.org/10.1093/qmathj/49.1.105
A + B = C and big III's

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Assuming standard conjectures we show that there exist elliptic curves with Tate-Shafarevich group of order essentially as large as the square root of the conductor. We present some concrete examples of such elliptic curves, related to good examples for the ABC-Conjecture.

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Subjects: Pure Mathematics

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