Heidi Goodson

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20242026

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4 papers · 1 filter

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…

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

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

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