Austyn Simpson

activity

20192026

most cited

F

-nilpotent rings and permanence properties

9 citations · 11 across the 12 of their papers we have counts for

collaborators

Showing 2023Show all

4 papers · 1 filter

math.AC2023

Uniform arithmetic in local rings via ultraproducts

Clay Adams, Francesca Cantor, Anese Gashi +4

We reinterpret various properties of Noetherian local rings via the existence of some $n$ -ary numerical function satisfying certain uniform bounds. We provide such characterization…

math.AC2023

ACC for $F$ -signature: a likely counterexample

Clay Adams, Theodore J. Sandstrom, Austyn Simpson

Let $k = F_{2}$ and let $0 \neq = α \in k$ . We present a conjecture supported by computer experimentation involving the Brenner-Monsky quartic $g_α=α…

math.AC2023

Flat morphisms with regular fibers do not preserve $F$ -rationality

Eamon Quinlan-Gallego, Austyn Simpson, Anurag K. Singh

For each positive prime integer $p$ we construct a standard graded $F$ -rational ring $R$ , over a field $K$ of characteristic $p$ , such that $R \otimes_{K} K$ is not $F$ -rati…

math.AG2023

On $F$ -pure inversion of adjunction

Thomas Polstra, Austyn Simpson, Kevin Tucker

We analyze adjunction and inversion of adjunction for the $F$ -purity of divisor pairs in characteristic $p > 0$ . In this vein, we give a complete answer for principal divisors unde…

Uniform arithmetic in local rings via ultraproducts

ACC for F-signature: a likely counterexample

Flat morphisms with regular fibers do not preserve F-rationality

On F-pure inversion of adjunction

ACC for $F$ -signature: a likely counterexample

Flat morphisms with regular fibers do not preserve $F$ -rationality

On $F$ -pure inversion of adjunction