Elliptic curves with bounded ranks in function field towers

Details Elliptic curves with bounded ranks in function field towers Elliptic curves with bounded ranks in function field towers

2011-05-30

arxiv.org/abs/1105.6083v1

Mathematics

Number Theory

Scientific paper

Let $k$ denote an algebraically closed field. We revisit a construction of the author of families of elliptic curves over the rational function field $k(t)$. Combining a combinatorial analysis with a rank formula of Ulmer we prove that, for all but finitely many families of these curves, the Mordell-Weil groups over $k(t^{1/d})$ have rank zero, as $d$ ranges over positive integers prime to the characteristic of $k$.

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