Jack J. Garzella

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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.NT2025

Abhyankar valuations, Prüfer-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…