On localization of tight closure in line-S4 quartics

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 F2‾ in which tight closure does not commute with localization. Our methods involve a tiling argument using Sierpiński triangles, as well as an ins...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2024-09, Vol.228 (9), p.107682, Article 107682
Main Authors: Borevitz, Levi, Nader, Naima, Sandstrom, Theodore J., Shapiro, Amelia, Simpson, Austyn, Zomback, Jenna
Format: Article
Language:English
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Summary: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 F2‾ in which tight closure does not commute with localization. Our methods involve a tiling argument using Sierpiński triangles, as well as an inspection of a certain dynamical system in characteristic two.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2024.107682