P. A. Helminck

activity

20162026

most citedTropicalizing abelian covers of algebraic curves

9 citations · 21 across the 18 of their papers we have counts for

collaborators

Showing 2018Show all

5 papers · 1 filter

math.AG2018★ 1 cited

Faithful tropicalizations of elliptic curves using minimal models and inflection points

Paul Alexander Helminck

We give an elementary proof of the fact that any elliptic curve $E$ over an algebraically closed non-archimedean field $K$ with residue characteristic $\neq = 2, 3$ and with $v(j(E))…

math.AG2018

Skeletal filtrations of the fundamental group of a non-archimedean curve

Paul Alexander Helminck

In this paper we study skeleta of residually tame coverings of a marked curve over a non-archimedean field. We first generalize a result by Liu and Lorenzini by proving a simultane…

math.AG2018

Semisimple pointed isogeny graphs for abelian varieties

Paul Alexander Helminck

In this paper we show that if $ϕ_{i} : A_{i} \to A$ is a semisimple pointed $K$ -rational $ℓ$ -isogeny graph of order $n$ for a prime $ℓ$ , then the group of $ℓ$ -torsio…

math.AG2018

Torsion points on elliptic curves and tame semistable coverings

P. A. Helminck

In this paper, we study tame Galois coverings of semistable models that arise from torsion points on elliptic curves. These coverings induce Galois morphisms of intersection graphs…

math.NT2018★ 4 cited

Tribonacci numbers and primes of the form $p = x^{2} + 11 y^{2}$

Tim Evink, Paul Alexander Helminck

In this paper we show that for any prime number $p$ not equal to $11$ or $19$ , the Tribonacci number $T_{p - 1}$ is divisible by $p$ if and only if $p$ is of the form $x^{2} + 11 y^{2}$ . We…

Faithful tropicalizations of elliptic curves using minimal models and inflection points

Skeletal filtrations of the fundamental group of a non-archimedean curve

Semisimple pointed isogeny graphs for abelian varieties

Torsion points on elliptic curves and tame semistable coverings

Tribonacci numbers and primes of the form p=x2+11y2

Tribonacci numbers and primes of the form $p = x^{2} + 11 y^{2}$