Jack J. Garzella

collaborators

5 papers

math.NT2026

Abhyankar valuations, PrÃ¼fer-Manis valuations, and perfectoid Tate algebras

Dimitri Dine, Jack J Garzella

Let $K$ be a perfectoid field. We describe all quotient fields of the perfectoid Tate algebra\begin{equation*}T_{n,K}^{\text{perfd}}=K\langle X_{1}^{1/p^{\infty}},\dots, X_{n}^{1/p…

math.NT2026

Newton strata realization for hypersurfaces via explicit p-adic cohomology

Ryan Batubara, Jack J Garzella, Yongyuan Huang +1

Let $X$ be a smooth projective hypersurface over a finite field $k$ of characteristic $p$ . We address the problem of practically computing the zeta function $Z (X, T)$ of $X$ (equiva…

math.AC2025

$F$ -intersection flatness of dagger and Berkovich Tate algebras

Rankeya Datta, Jack J Garzella, Kevin Tucker

We show, using the techniques developed in arXiv:2504.06444 and arXiv:2305.11139, that dagger algebras and Tate algebras in the sense of Berkovich in prime characteristic $p > 0$ h…

math.AC2025

On F-pure thresholds and quasi-F-purity of hypersurfaces

Jack J Garzella, Vignesh Jagathese

We show that quasi- $F$ -pure but not $F$ -pure isolated quasi-homogeneous hypersurface singularities necessarily have $F$ -pure threshold $1 - \frac{1}{p}$ . This extends work of Bhatt…

math.AG2025

K3 surfaces of any Artin-Mazur height over $F_{5}$ and $F_{7}$ via quasi- $F$ -split singularities and GPU acceleration

Ryan Batubara, Jack J Garzella, Alex Pan

We develop a fast algorithm to calculate the Artin-Mazur height (equivalently, the quasi- $F$ -split height) of a Calabi-Yau hypersurface, building on the work in arXiv:2204.10076. W…