1. CMB 2009 (vol 53 pp. 58)
|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)
|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)
|Linear Relations Among the Values of Canonical Heights from the Existence of Non-Trivial Endomorphisms|
|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 $A(k)$.