Heidi Goodson

activity

20242026

collaborators

10 papers

math.NT2026

Ekedahl-Oort strata with a superspecial factor in unitary Shimura varieties

Emerald Andrews, Deewang Bhamidipati, Heidi Goodson +2

Let $k$ be an algebraically closed field of characteristic $p > 2$ and let $O_{K}$ be an imaginary quadratic order in which $p$ is inert. For any $a, b \in Z_{\geq 0}$ …

math.NT2026

On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons

Emerald Andrews, Deewang Bhamidipati, Maria Fox +3

In this paper, we give a complete classification of indecomposable Ekedahl--Oort strata of Shimura varieties associated to the unitary group $GU (a, b)$ over an odd inert p…

math.NT2025

Degeneracy and Sato-Tate groups of $y^{2} = x^{p^{2}} - 1$

Justin Chen, Heidi Goodson, Rezwan Hoque +1

We say that an abelian variety is degenerate if its Hodge ring is not generated by divisor classes. Degeneracy leads to some interesting challenges when computing Sato-Tate groups,…

math.NT2025

The Ekedahl-Oort and Newton stratification of the $GU (3, 2)$ Shimura variety

Emerald Andrews, Deewang Bhamidipati, Maria Fox +3

This paper concerns the characteristic- $p$ fibers of $GU (3, 2)$ Shimura varieties. Such Shimura varieties parametrize abelian varieties in characteristic $p$ of dimension $…

math.NT2025

Analogues of Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups

Emerald Andrews, Deewang Bhamidipati, Maria Fox +3

Let $p$ be a prime and $k$ an algebraically closed field of characteristic $p$ . Two invariants worthy of study for a $p$ -divisible group $X$ over $k$ are its isogeny cutoff…

math.NT2025

Monodromy groups and exceptional Hodge classes, II: Sato-Tate groups

Andrea Gallese, Heidi Goodson, Davide Lombardo

Denote by $J_{m}$ the Jacobian variety of the hyperelliptic curve defined by the affine equation $y^{2} = x^{m} + 1$ over $Q$ , where $m \geq 3$ is a fixed positive integer. In this…

math.NT2024

Sato-Tate Groups and Distributions of $y^{ℓ} = x (x^{ℓ} - 1)$

Heidi Goodson, Rezwan Hoque

Let $C_{ℓ} / Q$ denote the curve with affine model $y^{ℓ} = x (x^{ℓ} - 1)$ , where $ℓ \geq 3$ is prime. In this paper we study the limiting distributions of the normalized $L$ …

math.NT2024

Monodromy groups and exceptional Hodge classes, I: Fermat Jacobians

Andrea Gallese, Heidi Goodson, Davide Lombardo

Denote by $J_{m}$ the Jacobian variety of the hyperelliptic curve defined by the affine equation $y^{2} = x^{m} + 1$ over $Q$ , where $m \geq 3$ is a fixed positive integer. We compu…

math.NT2024

Ekedahl-Oort strata in the $GU (q - 2, 2)$ Shimura variety

Emerald Andrews, Deewang Bhamidipati, Maria Fox +3

This paper concerns the characteristic- $p$ fibers of $GU (q - 2, 2)$ Shimura varieties, which classify abelian varieties with additional structure. These Shimura varieties adm…

math.NT2024

On invariants of Artin-Schreier curves

Juanita Duque-Rosero, Heidi Goodson, Elisa Lorenzo García +2

The main goal of this article is to expand the theory of invariants of Artin-Schreier curves by giving a complete classification in genus 3 and 4. To achieve this goal, we first es…

Ekedahl-Oort strata with a superspecial factor in unitary Shimura varieties

On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons

Degeneracy and Sato-Tate groups of y2=xp2−1

The Ekedahl-Oort and Newton stratification of the GU(3,2) Shimura variety

Analogues of Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups

Monodromy groups and exceptional Hodge classes, II: Sato-Tate groups

Sato-Tate Groups and Distributions of yℓ=x(xℓ−1)

Monodromy groups and exceptional Hodge classes, I: Fermat Jacobians

Ekedahl-Oort strata in the GU(q−2,2) Shimura variety

On invariants of Artin-Schreier curves

Degeneracy and Sato-Tate groups of $y^{2} = x^{p^{2}} - 1$

The Ekedahl-Oort and Newton stratification of the $GU (3, 2)$ Shimura variety

Sato-Tate Groups and Distributions of $y^{ℓ} = x (x^{ℓ} - 1)$

Ekedahl-Oort strata in the $GU (q - 2, 2)$ Shimura variety