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Let $\mathscr{k}=\overline{\mathbb{F}_2}$ and let $0\neq\alpha\in \mathscr{k}$. We present a conjecture supported by computer experimentation involving the Brenner-Monsky quartic $g_\alpha=\alpha x^2y^2+z^4+xyz^2+(x^3+y^3)z\in \mathscr{k}[[x,y,z]]$.
Externí odkaz:
http://arxiv.org/abs/2309.07901
Autor:
Borevitz, Levi, Nader, Naima, Sandstrom, Theodore J., Shapiro, Amelia, Simpson, Austyn, Zomback, Jenna
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
Externí odkaz:
http://arxiv.org/abs/2211.03220
Autor:
Borevitz, Levi, Nader, Naima, Sandstrom, Theodore J., Shapiro, Amelia, Simpson, Austyn, Zomback, Jenna
Publikováno v:
In Journal of Pure and Applied Algebra September 2024 228(9)
