Austyn Simpson

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math.AC2024

Noncatenary splinters in prime characteristic

S. Loepp, Austyn Simpson

We construct a local Noetherian splinter (in fact, a weakly $F$ -regular domain) in prime characteristic which is not catenary, which we view as an analogue of a theorem of Ogoma in…

math.AC2024

The perfection can be a non-coherent GCD domain

Austyn Simpson

We show that there exists a complete local Noetherian normal domain of prime characteristic whose perfection is a non-coherent GCD domain, answering a question of Patankar in the n…

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…

Noncatenary splinters in prime characteristic

The perfection can be a non-coherent GCD domain

Uniform arithmetic in local rings via ultraproducts

ACC for F-signature: a likely counterexample

ACC for $F$ -signature: a likely counterexample