David Zureick-Brown

activity

20122026

most citedSporadic Cubic Torsion

44 citations · 124 across the 20 of their papers we have counts for

collaborators

24 papers

math.NT2026

$7$ -adic Galois representations of elliptic curves over the rationals via Kummer descent

Santiago Arango-Piñeros, David Zureick-Brown

We show that the two modular curves of level $49$ and genus $9$ left open by the work of Rouse, Sutherland and Zureick-Brown, and of Furio and Lombardo, have no non-CM rational poi…

math.AG2026

The Dimension Conjecture Implies The Jacobi Bound Conjecture

Taylor Dupuy, David Zureick-Brown

We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.

math.AG2026

The Jacobi Bound Conjecture for Generically Reduced Differential Schemes

Taylor Dupuy, David Zureick-Brown

We prove the Strong Jacobi Bound Conjecture for generically reduced components of differential schemes.

math.AG2025

The Degree of Irrationality of del Pezzo Surfaces

Adam Logan, Anthony Várilly-Alvarado, David Zureick-Brown

For an irreducible variety $X$ over a field $k$ , the degree of irrationality $irr_{k} X$ is the minimal degree of a dominant rational map $X \dashrightarrow \mathbb{P}…

math.AG2025

Wild Stacky Curves and Rings of Mod p Modular Forms

Andrew Kobin, David Zureick-Brown

We extend work of Voight and the second author to compute the log canonical ring of a wild stacky curve over a field of characteristic $p > 0$ , which allows us to compute rings of…

math.NT2021

Angle ranks of abelian varieties

Taylor Dupuy, Kiran S. Kedlaya, David Zureick-Brown

Using the formalism of Newton hyperplane arrangements, we resolve the open questions regarding angle rank left over from [DKRV20]. As a consequence we end up generalizing theorems…

math.NT2021★ 4 cited

Heights on stacks and a generalized Batyrev-Manin-Malle conjecture

Jordan S. Ellenberg, Matthew Satriano, David Zureick-Brown

We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual n…

math.NT2021★ 29 cited

$ℓ$ -adic images of Galois for elliptic curves over $Q$

Jeremy Rouse, Andrew V. Sutherland, David Zureick-Brown

We discuss the $ℓ$ -adic case of Mazur's "Program B" over $Q$ , the problem of classifying the possible images of $ℓ$ -adic Galois representations attached to elliptic…

math.NT2020★ 44 cited

Sporadic Cubic Torsion

Maarten Derickx, Anastassia Etropolski, Mark van Hoeij +2

Let $K$ be a number field, and let $E / K$ be an elliptic curve over $K$ . The Mordell--Weil theorem asserts that the $K$ -rational points $E (K)$ of $E$ form a finitely generated abeli…

math.NT2019★ 8 cited

A predicted distribution for Galois groups of maximal unramified extensions

Yuan Liu, Melanie Matchett Wood, David Zureick-Brown

We consider the distribution of the Galois groups $Gal (K^{un} / K)$ of maximal unramified extensions as $K$ ranges over $Γ$ -extensions of $Q$ o…

math.NT2018

Deligne--Illusie Classes as Arithmetic Kodaira--Spencer Classes

Taylor Dupuy, David Zureick-Brown

Faltings showed that "arithmetic Kodaira--Spencer classes" satisfying a certain compatibility axiom cannot exist. By modifying his definitions slightly, we show that the Deligne--I…

math.AG2017

Total $p$ -differentials on schemes over $Z / p^{2}$

Taylor Dupuy, Eric Katz, Joseph Rabinoff +1

For a scheme $X$ defined over the length $2$ $p$ -typical Witt vectors $W_{2} (k)$ of a characteristic $p$ field, we introduce total $p$ -differentials which interpolate between Frobeni…

math.CO2017

Chip-firing groups of iterated cones

Morgan V. Brown, Jackson S. Morrow, David Zureick-Brown

Let $Γ$ be a finite graph and let $Γ_{n}$ be the " $n$ th cone over $Γ$ " (i.e., the join of $Γ$ and the complete graph $K_{n}$ ). We study the asymptotic structure of the chip-firing grou…

math.NT2016

Diophantine and tropical geometry, and uniformity of rational points on curves

Eric Katz, Joseph Rabinoff, David Zureick-Brown

We describe recent work connecting combinatorics and tropical/non-Archimedean geometry to Diophantine geometry, particularly the uniformity conjectures for rational points on curve…

math.NT2015★ 27 cited

Uniform bounds for the number of rational points on curves of small Mordell--Weil rank

Eric Katz, Joseph Rabinoff, David Zureick-Brown

Let $X$ be a curve of genus $g \geq 2$ over a number field $F$ of degree $d = [F : Q]$ . The conjectural existence of a uniform bound $N (g, d)$ on the number $# X (F)$ of $F$ -rational po…

math.AG2015★ 2 cited

The canonical ring of a stacky curve

John Voight, David Zureick-Brown

Generalizing the classical theorems of Max Noether and Petri, we describe generators and relations for the canonical ring of a stacky curve, including an explicit Gröbner basis. We…

math.NT2014★ 5 cited

A heuristic for the distribution of point counts for random curves over a finite field

Jeffrey D. Achter, Daniel Erman, Kiran S. Kedlaya +2

How many rational points are there on a random algebraic curve of large genus $g$ over a given finite field $F_{q}$ ? We propose a heuristic for this question motivated by a…

math.AG2014★ 3 cited

Cohomology with closed support on the overconvergent site

David Zureick-Brown

Using the notions of open/closed subtopoi of SGA, we define a notion of cohomology with support in a closed subscheme on the overconvergent site, and show that this agrees with the…

math.NT2014

Elliptic curves over $Q$ and 2-adic images of Galois

Jeremy Rouse, David Zureick-Brown

We give a classification of all possible $2$ -adic images of Galois representations associated to elliptic curves over $Q$ . To this end, we compute the 'arithmetically maxi…

math.AG2013

Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex

Christopher Davis, David Zureick-Brown

In their paper which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give integral cohomology group…

math.AG2012★ 1 cited

Formal GAGA for good moduli spaces

Anton Geraschenko, David Zureick-Brown

We prove formal GAGA for good moduli space morphisms under an assumption of "enough vector bundles" (which holds for instance for quotient stacks). This supports the philosophy tha…

math.AG2012

Cohomological descent on the overconvergent site

David Zureick-Brown

We prove that cohomological descent holds for finitely presented crystals on the overconvergent site with respect to proper or fppf hypercovers.

math.NT2012

The Chabauty-Coleman bound at a prime of bad reduction and clifford bounds for geometric rank functions

Eric Katz, David Zureick-Brown

Let X be a curve over a number field K with genus g>=2, $\pp$ a prime of O_K over an unramified rational prime p>2r, J the Jacobian of X, r=rank J(K), and $\scrX$ a regular proper…

math.NT2012★ 1 cited

Random Dieudonne modules, random p-divisible groups, and random curves over finite fields

Bryden Cais, Jordan S. Ellenberg, David Zureick-Brown

We describe a probability distribution on isomorphism classes of principally quasi-polarized p-divisible groups over a finite field k of characteristic p which can reasonably be th…

7-adic Galois representations of elliptic curves over the rationals via Kummer descent

The Dimension Conjecture Implies The Jacobi Bound Conjecture

The Jacobi Bound Conjecture for Generically Reduced Differential Schemes

The Degree of Irrationality of del Pezzo Surfaces

Wild Stacky Curves and Rings of Mod p Modular Forms

Angle ranks of abelian varieties

Heights on stacks and a generalized Batyrev-Manin-Malle conjecture

ℓ-adic images of Galois for elliptic curves over Q

Sporadic Cubic Torsion

A predicted distribution for Galois groups of maximal unramified extensions

Deligne--Illusie Classes as Arithmetic Kodaira--Spencer Classes

Total p-differentials on schemes over Z/p2

Chip-firing groups of iterated cones

Diophantine and tropical geometry, and uniformity of rational points on curves

Uniform bounds for the number of rational points on curves of small Mordell--Weil rank

The canonical ring of a stacky curve

A heuristic for the distribution of point counts for random curves over a finite field

Cohomology with closed support on the overconvergent site

Elliptic curves over Q and 2-adic images of Galois

Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex

Formal GAGA for good moduli spaces

Cohomological descent on the overconvergent site

The Chabauty-Coleman bound at a prime of bad reduction and clifford bounds for geometric rank functions

Random Dieudonne modules, random p-divisible groups, and random curves over finite fields

$7$ -adic Galois representations of elliptic curves over the rationals via Kummer descent

$ℓ$ -adic images of Galois for elliptic curves over $Q$

Total $p$ -differentials on schemes over $Z / p^{2}$

Elliptic curves over $Q$ and 2-adic images of Galois