On Localization of Tight Closure in Line-$S_4$ Quartics
Commutative Algebra
2022-11-08 v1 Algebraic Geometry
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 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.
Keywords
Cite
@article{arxiv.2211.03220,
title = {On Localization of Tight Closure in Line-$S_4$ Quartics},
author = {Levi Borevitz and Naima Nader and Theodore J. Sandstrom and Amelia Shapiro and Austyn Simpson and Jenna Zomback},
journal= {arXiv preprint arXiv:2211.03220},
year = {2022}
}
Comments
Written during the 2022 SMALL REU at Williams College. Comments welcome