当前位置: X-MOL 学术J. Algebra › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The uniform symbolic topology property for diagonally F-regular algebras
Journal of Algebra ( IF 0.9 ) Pub Date : 2020-04-01 , DOI: 10.1016/j.jalgebra.2019.11.017
Javier Carvajal-Rojas , Daniel Smolkin

Let $k$ be a field of positive characteristic. Building on the work of the second named author, we define a new class of $k$-algebras, called diagonally $F$-regular algebras, for which the so-called Uniform Symbolic Topology Property (USTP) holds effectively. We show that this class contains all essentially smooth $k$-algebras. We also show that this class contains certain singular algebras, such as the affine cone over $\mathbb{P}^r_{k} \times \mathbb{P}^s_{k}$, when $k$ is perfect. By reduction to positive characteristic, it follows that USTP holds effectively for the affine cone over $\mathbb{P}^r_{\mathbb{C}} \times \mathbb{P}^s_{\mathbb{C}}$ and more generally for complex varieties of diagonal $F$-regular type.

中文翻译:

对角F-正则代数的统一符号拓扑性质

令 $k$ 是一个积极特征的领域。基于第二位作者的工作,我们定义了一类新的 $k$-代数,称为对角线 $F$-正则代数,所谓的统一符号拓扑属性 (USTP) 对此有效。我们表明该类包含所有基本平滑的 $k$-代数。我们还展示了这个类包含某些奇异代数,例如 $\mathbb{P}^r_{k} \times \mathbb{P}^s_{k}$ 上的仿射锥,当 $k$ 是完美的。通过归约到正特征,USTP 对 $\mathbb{P}^r_{\mathbb{C}} \times \mathbb{P}^s_{\mathbb{C}}$ 和更一般地用于对角线 $F$-regular 类型的复杂变体。
更新日期:2020-04-01
down
wechat
bug