Caleb Springer

activity

20182026

most citedEvery finite abelian group is the group of rational points of an ordinary abelian variety over

F_{2}

F_{3}

and

F_{5}

3 citations · 11 across the 12 of their papers we have counts for

collaborators

12 papers

math.NT2026

Definability and undecidability via the torsion subgroup of units

Caleb Springer

In this paper, we prove that $Z$ is first-order definable in the ring of integers $Z^{ab}$ of the maximal abelian extension $Q^{ab}$ of $\m…

math.NT2025

Isogeny graphs of abelian varieties and singular ideals in orders

Sarah Arpin, Stefano Marseglia, Caleb Springer

Famously, Kohel proved that isogeny graphs of ordinary elliptic curves are beautifully structured objects, now called volcanos. We prove graph structural theorems for abelian varie…

math.NT2024

First-order definitions of rings of integral functions over algebraic extensions of function fields and undecidability

Alexandra Shlapentokh, Caleb Springer

In this paper, we study questions of definability and decidability for infinite algebraic extensions $K$ of $F_{p} (t)$ and their subrings of $S$ -integral fun…

math.NT2022

Abelian varieties over finite fields and their groups of rational points

Stefano Marseglia, Caleb Springer

We study the groups of rational points of abelian varieties defined over a finite field $F_{q}$ whose endomorphism rings are commutative, or, equivalently, whose isogeny cl…

math.NT2022★ 3 cited

Definability and decidability for rings of integers in totally imaginary fields

Caleb Springer

We show that the ring of integers of $Q^{tr}$ is existentially definable in the ring of integers of $Q^{tr} (i)$ , where $Q^{tr}$ deno…

math.NT2021★ 3 cited

Every finite abelian group is the group of rational points of an ordinary abelian variety over $F_{2}$ , $F_{3}$ and $F_{5}$

Stefano Marseglia, Caleb Springer

We show that every finite abelian group $G$ occurs as the group of rational points of an ordinary abelian variety over $F_{2}$ , $F_{3}$ and $F_{5}$ . We produce…

math.NT2021

Doubly isogenous genus-2 curves with $D_{4}$ -action

Vishal Arul, Jeremy Booher, Steven R. Groen +5

We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C' are curves over…

math.NT2020★ 2 cited

A topological approach to undefinability in algebraic extensions of $Q$

Kirsten Eisentraeger, Russell Miller, Caleb Springer +1

For any subset $Z \subseteq Q$ , consider the set $S_{Z}$ of subfields $L \subseteq Q$ which contain a co-infinite subset $C \subseteq L$ that is universal…

math.NT2020★ 3 cited

The Structure of the Group of Rational Points of an Abelian Variety over a Finite Field

Caleb Springer

Let $A$ be a simple abelian variety of dimension $g$ defined over a finite field $F_{q}$ with Frobenius endomorphism $π$ . This paper describes the structure of the group of…

math.NT2020

Restrictions on Weil polynomials of Jacobians of hyperelliptic curves

Edgar Costa, Ravi Donepudi, Ravi Fernando +3

Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hypere…

math.NT2019

Undecidability, unit groups, and some totally imaginary infinite extensions of $Q$

Caleb Springer

We produce new examples of totally imaginary infinite extensions of $Q$ which have undecidable first-order theory by generalizing the methods used by Martinez-Ranero, Utre…

math.NT2018

Computing the endomorphism ring of an ordinary abelian surface over a finite field

Caleb Springer

We present a new algorithm for computing the endomorphism ring of an ordinary abelian surface over a finite field which is subexponential and generalizes an algorithm of Bisson and…

Definability and undecidability via the torsion subgroup of units

Isogeny graphs of abelian varieties and singular ideals in orders

First-order definitions of rings of integral functions over algebraic extensions of function fields and undecidability

Abelian varieties over finite fields and their groups of rational points

Definability and decidability for rings of integers in totally imaginary fields

Every finite abelian group is the group of rational points of an ordinary abelian variety over F2​, F3​ and F5​

Doubly isogenous genus-2 curves with D4​-action

A topological approach to undefinability in algebraic extensions of Q

The Structure of the Group of Rational Points of an Abelian Variety over a Finite Field

Restrictions on Weil polynomials of Jacobians of hyperelliptic curves

Undecidability, unit groups, and some totally imaginary infinite extensions of Q

Computing the endomorphism ring of an ordinary abelian surface over a finite field

Every finite abelian group is the group of rational points of an ordinary abelian variety over $F_{2}$ , $F_{3}$ and $F_{5}$

Doubly isogenous genus-2 curves with $D_{4}$ -action

A topological approach to undefinability in algebraic extensions of $Q$

Undecidability, unit groups, and some totally imaginary infinite extensions of $Q$