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-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 h…
Abhyankar valuations, Prüfer-Manis valuations, and perfectoid Tate algebras
Dimitri Dine, Jack J Garzella
Let 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…
On F-pure thresholds and quasi-F-purity of hypersurfaces
Jack J Garzella, Vignesh Jagathese
We show that quasi--pure but not -pure isolated quasi-homogeneous hypersurface singularities necessarily have -pure threshold . This extends work of Bhatt…
K3 surfaces of any Artin-Mazur height over and via quasi--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--split height) of a Calabi-Yau hypersurface, building on the work in arXiv:2204.10076. W…