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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24 papers · 1 filter

math.NT2026

Minimal $a$ -numbers of Artin--Schreier covers of ordinary curves

Bryden Cais, Douglas Ulmer

Let $k$ be a perfect field of characteristic $p > 0$ , and let $d$ be a positive integer not divisible by $p$ . We define a non-empty Zariski open subset $U$ of the space of polynomial…

math.NT2023

$p$ -torsion for unramified Artin--Schreier covers of curves

Bryden Cais, Douglas Ulmer

Let $Y \to X$ be an unramified Galois cover of curves over a perfect field $k$ of characteristic $p > 0$ with $Gal (Y / X) ≅ Z / p Z$ , and let $J_{X}$ and $J_{Y}$ b…

math.NT2021

Every $B T_{1}$ group scheme appears in a Jacobian

Rachel Pries, Douglas Ulmer

Let $p$ be a prime number and let $k$ be an algebraically closed field of characteristic $p$ . A $B T_{1}$ group scheme over $k$ is a finite commutative group scheme which arises as th…

math.NT2020★ 1 cited

On $B T_{1}$ group schemes and Fermat Jacobians

Rachel Pries, Douglas Ulmer

Let $p$ be a prime number and let $k$ be an algebraically closed field of characteristic $p$ . A $B T_{1}$ group scheme over $k$ is a finite commutative group scheme which arises as th…

math.NT2019★ 5 cited

On the arithmetic of a family of twisted constant elliptic curves

Richard Griffon, Douglas Ulmer

Let $F_{r}$ be a finite field of characteristic $p > 3$ . For any power $q$ of $p$ , consider the elliptic curve $E = E_{q, r}$ defined by $y^{2} = x^{3} + t^{q} - t$ over $K=\mathbb{F}_r(t…

math.NT2018★ 5 cited

On the Brauer-Siegel ratio for abelian varieties over function fields

Douglas Ulmer

Hindry has proposed an analogue of the classical Brauer-Siegel theorem for abelian varieties over global fields. Roughly speaking, it says that the product of the regulator of the…

Minimal a-numbers of Artin--Schreier covers of ordinary curves

p-torsion for unramified Artin--Schreier covers of curves

Every BT1​ group scheme appears in a Jacobian