J. Booher

activity

20162026

most citedMinimally Ramified Deformations when

ℓ \neq = p

10 citations · 31 across the 20 of their papers we have counts for

collaborators

21 papers

math.NT2026

Computing Crystalline Cohomology and p-Divisible Groups for Curves over Finite Fields

Jeremy Booher

Let $X$ be a smooth projective curve over a finite field of characteristic $p$ . We describe and implement a practical algorithm for computing the $p$ -divisible group $Jac(X)[p^\inf…

math.NT2025

Ekedahl-Oort types of $Z /2 Z$ -covers in characteristic $2$

Jeremy Booher, Steven R. Groen, Joe Kramer-Miller

In this article we study the Ekedahl-Oort types of $Z /2 Z$ -Galois covers $π : Y \to X$ in characteristic two. When the base curve $X$ is ordinary, we show that the E…

math.NT2025

Supersingular curves via the Shimura--Taniyama method

Jeremy Booher, Rachel Pries

For a curve which admits an abelian cover of the projective line branched at three points, we study when its reduction to positive characteristic is supersingular. Using the method…

math.NT2024

Producing supersingular curves of genus five

Jeremy Booher, Rachel Pries

For a prime $p$ congruent to three modulo four, we prove that there exists a smooth curve of genus five in characteristic $p$ that is supersingular. We produce this curve as an unr…

math.NT2024

Iwasawa theory of Frobenius-torsion class group schemes

Jeremy Booher, Bryden Cais, Joe Kramer-Miller +1

We establish a new Iwasawa theory for the kernel of Frobenius on Jacobians of curves in geometric $Z_{p}$ -towers over the projective line in characteristic $p$ , thereby prov…

math.NT2024

Higher a-numbers in $Z_{p}$ -towers via Counting Lattice Points

Jeremy Booher, Jack Hsieh, Rakesh Rivera +3

Booher, Cais, Kramer-Miller and Upton study a class of $Z_{p}$ -tower of curves in characteristic $p$ with ramification controlled by an integer $d$ . In the special case that…

math.NT2024

Doubly isogenous curves of genus two with a rational action of $D_{6}$

Jeremy Booher, Everett W. Howe, Andrew V. Sutherland +1

Let $C$ and $C^{'}$ be curves over a finite field $K$ , provided with embeddings $ι$ and $ι^{'}$ into their Jacobian varieties. Let $D \to C$ and $D^{'} \to C^{'}$ be the pullbacks (via these emb…

math.NT2022

Lifting $G$ -Valued Galois Representations when $ℓ \neq = p$

Jeremy Booher, Sean Cotner, Shiang Tang

In this paper we study the universal lifting spaces of local Galois representations valued in arbitrary reductive group schemes when $ℓ \neq = p$ . In particular, under certain tec…

math.NT2022★ 1 cited

Failing to hash into supersingular isogeny graphs

Jeremy Booher, Ross Bowden, Javad Doliskani +12

An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equation…

math.NT2021★ 2 cited

Iwasawa Theory for $p$ -torsion Class Group Schemes in Characteristic $p$

Jeremy Booher, Bryden Cais

We investigate a novel geometric Iwasawa theory for $Z_{p}$ -extensions of function fields over a perfect field $k$ of characteristic $p > 0$ by replacing the usual study of $p…

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★ 1 cited

Recovering affine curves over finite fields from $L$ -functions

Jeremy Booher, José Felipe Voloch

Let $K$ be the function field of a curve over a finite field of odd characteristic. We investigate using $L$ -functions of Galois extensions of $K$ to effectively recover $K$ . When…

math.NT2020

G-Valued Crystalline Deformation Rings in the Fontaine-Laffaille Range

Jeremy Booher, Brandon Levin

Let $G$ be a split reductive group over the ring of integers in a $p$ -adic field with residue field $F$ . Fix a representation $ρ$ of the absolute Galois group of…

math.NT2020

Tamely Ramified Covers of the Projective Line with Alternating and Symmetric Monodromy

Renee Bell, Jeremy Booher, William Y. Chen +1

Let $k$ be an algebraically closed field of characteristic $p$ and let $X$ the projective line over $k$ with three points removed. We investigate which finite groups $G$ can arise…

math.NT2020

Realizing Artin-Schreier covers of curves with minimal Newton polygons in positive characteristic

Jeremy Booher, Rachel Pries

Suppose $X$ is a smooth projective connected curve defined over an algebraically closed field $k$ of characteristic $p > 0$ and $B \subset X (k)$ is a finite, possibly empty, set of p…

math.NT2020

Recovering algebraic curves from L-functions of Hilbert class fields

Jeremy Booher, José Felipe Voloch

In this paper, we prove that a smooth hyperbolic projective curve over a finite field can be recovered from L-functions associated to the Hilbert class field of the curve and its c…

math.NT2020★ 2 cited

Realizing Artin-Schreier Covers with Minimal $a$ -numbers in Positive Characteristic

Fiona Abney-McPeek, Hugo Berg, Jeremy Booher +8

Suppose $X$ is a smooth projective connected curve defined over an algebraically closed field of characteristic $p > 0$ and $B \subset X$ is a finite, possibly empty, set of points.…

math.NT2018★ 10 cited

Minimally Ramified Deformations when $ℓ \neq = p$

Jeremy Booher

Let $p$ and $ℓ$ be distinct primes, and $ρ$ be an orthogonal or symplectic representation of the absolute Galois group of an $ℓ$ -adic field over a finite field of characteris…

math.NT2018

a-Numbers of Curves in Artin-Schreier Covers

Jeremy Booher, Bryden Cais

Let $π : Y \to X$ be a branched $Z / p Z$ -cover of smooth, projective, geometrically connected curves over a perfect field of characteristic $p > 0$ . We investigate th…

math.NT2017★ 6 cited

G-Valued Galois Deformation Rings when $ℓ \neq = p$

Jeremy Booher, Stefan Patrikis

For a smooth group scheme $G$ over an extension of $Z_{p}$ such that the generic fiber of $G$ is reductive, we study the generic fiber of the Galois deformation ring for a $…

math.NT2016★ 9 cited

Producing Geometric Deformations of Orthogonal and Symplectic Galois Representations

Jeremy Booher

For a representation of the absolute Galois group of the rationals over a finite field of characteristic $p$ , we study the existence of a lift to characteristic zero that is geomet…

Computing Crystalline Cohomology and p-Divisible Groups for Curves over Finite Fields

Ekedahl-Oort types of Z/2Z-covers in characteristic 2

Supersingular curves via the Shimura--Taniyama method

Producing supersingular curves of genus five

Iwasawa theory of Frobenius-torsion class group schemes

Higher a-numbers in Zp​-towers via Counting Lattice Points

Doubly isogenous curves of genus two with a rational action of D6​

Lifting G-Valued Galois Representations when ℓ=p

Failing to hash into supersingular isogeny graphs

Iwasawa Theory for p-torsion Class Group Schemes in Characteristic p

Doubly isogenous genus-2 curves with D4​-action

Recovering affine curves over finite fields from L-functions

G-Valued Crystalline Deformation Rings in the Fontaine-Laffaille Range

Tamely Ramified Covers of the Projective Line with Alternating and Symmetric Monodromy

Realizing Artin-Schreier covers of curves with minimal Newton polygons in positive characteristic

Recovering algebraic curves from L-functions of Hilbert class fields

Realizing Artin-Schreier Covers with Minimal a-numbers in Positive Characteristic

Minimally Ramified Deformations when ℓ=p

a-Numbers of Curves in Artin-Schreier Covers

G-Valued Galois Deformation Rings when ℓ=p

Producing Geometric Deformations of Orthogonal and Symplectic Galois Representations

Ekedahl-Oort types of $Z /2 Z$ -covers in characteristic $2$

Higher a-numbers in $Z_{p}$ -towers via Counting Lattice Points

Doubly isogenous curves of genus two with a rational action of $D_{6}$

Lifting $G$ -Valued Galois Representations when $ℓ \neq = p$

Iwasawa Theory for $p$ -torsion Class Group Schemes in Characteristic $p$

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

Recovering affine curves over finite fields from $L$ -functions

Realizing Artin-Schreier Covers with Minimal $a$ -numbers in Positive Characteristic

Minimally Ramified Deformations when $ℓ \neq = p$

G-Valued Galois Deformation Rings when $ℓ \neq = p$