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arXiv · 2211.03220

On Localization of Tight Closure in Line-$S_4$ Quartics

Levi Borevitz·Naima Nader·Theodore J. Sandstrom·Amelia Shapiro·Austyn Simpson·Jenna Zomback
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Abstract

Building on work of Brenner and Monsky from 2010 and on a Hilbert-Kunz calculation of Monsky from 1998, we exhibit a novel example of a hypersurface over $\overline{\mathbb{F}_2}$ in which tight closure does not commute with localization. Our methods involve a surprising tiling argument using Sierpi\'nski triangles, as well as an inspection of a certain dynamical system in characteristic two.

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Levi Borevitz, Naima Nader, Theodore J. Sandstrom, Amelia Shapiro, Austyn Simpson, Jenna Zomback. 2022-11-06. On Localization of Tight Closure in Line-$S_4$ Quartics. https://arxiv.org/abs/2211.03220

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