Austyn Simpson

collaborators

5 papers

math.AC2026

$F$ -injectivity does not imply $F$ -fullness in normal domains

Alessandro De Stefani, Thomas Polstra, Austyn Simpson

We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are $F$ -injective but not $F$ -full. Along the way, we find ex…

math.AC2026

A Buchsbaum theory for Frobenius closure

Kriti Goel, Kyle Maddox, Lance Edward Miller +2

We give a partial characterization for when the difference $e (q) - ℓ_{R} (R / q^{F})$ is independent of the choice of parameter ideal $q \subseteq R$ in a…

math.AG2025

Bertini's theorem for $F$ -rational $F$ -pure singularities

Alessandro De Stefani, Thomas Polstra, Austyn Simpson

Let $k$ be an algebraically closed field of characteristic $p > 0$ , and let $X \subseteq P_{k}^{n}$ be a quasi-projective variety that is $F$ -rational and $F$ -pure. We prove that…

math.AC2025

Hilbert-Kunz multiplicity and $F$ -signature can disagree

Seungsu Lee, Suchitra Pande, Austyn Simpson

We compute the $F$ -signature function of the ample cone of any nontrivial ruled surface over $P_{k}^{1}$ where $k$ is an algebraically closed field of prime characteristic. As…

math.AC2025

On deformation of perfectoid purity in Gorenstein domains

Benjamin Baily, Karina Dovgodko, Austyn Simpson +1

If $(R, m)$ is a complete local ring of mixed characteristic $(0, p)$ and $R / pR$ is an $F$ -pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid…

F-injectivity does not imply F-fullness in normal domains

A Buchsbaum theory for Frobenius closure

Bertini's theorem for F-rational F-pure singularities

Hilbert-Kunz multiplicity and F-signature can disagree

On deformation of perfectoid purity in Gorenstein domains

$F$ -injectivity does not imply $F$ -fullness in normal domains

Bertini's theorem for $F$ -rational $F$ -pure singularities

Hilbert-Kunz multiplicity and $F$ -signature can disagree