Douglas Ulmer

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20012026

most citedGeometric non-vanishing

15 citations · 57 across the 25 of their papers we have counts for

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math.NT2010

Ranks of Jacobians in towers of function fields

Douglas Ulmer, Yuri G. Zarhin

Let $k$ be a field of characteristic zero and let $K = k (t)$ be the rational function field over $k$ . In this paper we combine a formula of Ulmer for ranks of certain Jacobians over…

math.NT2010

Explicit points on the Legendre curve

Douglas Ulmer

We study the elliptic curve E given by y^2=x(x+1)(x+t) over the rational function field k(t) and its extensions K_d=k(μ_d,t^{1/d}). When k is finite of characteristic p and d=p^f+1…

math.NT2010

On Mordell-Weil groups of Jacobians over function fields

Douglas Ulmer

We study the arithmetic of abelian varieties over $K = k (t)$ where $k$ is an arbitrary field. The main result relates Mordell-Weil groups of certain Jacobians over $K$ to homomorphis…