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Results 1 - 3 of 3 |
1. CMB 2009 (vol 53 pp. 58)
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Ranks in Families of Jacobian Varieties of Twisted Fermat Curves In this paper, we prove that the unboundedness of ranks in families of Jacobian varieties of twisted Fermat curves is equivalent to the divergence of certain infinite series.
Keywords:Fermat curve, Jacobian variety, elliptic curve, canonical height Categories:11G10, 11G05, 11G50, 14G05, 11G30, 14H45, 14K15 |
2. CMB 2005 (vol 48 pp. 428)
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Reduction of Elliptic Curves in Equal Characteristic~3 (and~2) and fibre type for elliptic curves
over discrete valued fields of equal characteristic~3.
Along the same lines, partial results are obtained
in equal characteristic~2.
Categories:14H52, 14K15, 11G07, 11G05, 12J10 |
3. CMB 2004 (vol 47 pp. 271)
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Linear Relations Among the Values of Canonical Heights from the Existence of Non-Trivial Endomorphisms We study the interplay between canonical heights and endomorphisms of an abelian
variety $A$ over a number field $k$. In particular we show that whenever the ring
of endomorphisms defined over $k$ is strictly larger than $\Z$ there will
be $\Q$-linear relations among the values of a canonical height pairing evaluated
at a basis modulo torsion of $A(k)$.
Categories:11G10, 14K15 |