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Search: MSC category 14K15 ( Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx] )

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1. CMB 2009 (vol 53 pp. 58)

Dąbrowski, Andrzej; Jędrzejak, Tomasz
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)

Miyamoto, Roland; Top, Jaap
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)

Naumann, Niko
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

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