Report
Arithmetic and geometric deformations of $F$-pure and $F$-regular singularities
| العنوان: | Arithmetic and geometric deformations of $F$-pure and $F$-regular singularities |
|---|---|
| المؤلفون: | Sato, Kenta, Takagi, Shunsuke |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, 13A35, 14B05, 14B07, 14D10, 14F18 |
| الوصف: | Given a normal $\mathbb{Q}$-Gorenstein complex variety $X$, we prove that if one spreads it out to a normal $\mathbb{Q}$-Gorenstein scheme $\mathcal{X}$ of mixed characteristic whose reduction $\mathcal{X}_p$ modulo $p$ has normal $F$-pure singularities for a single prime $p$, then $X$ has log canonical singularities. In addition, we show its analog for log terminal singularities, without assuming that $\mathcal{X}$ is $\mathbb{Q}$-Gorenstein, which is a generalization of a result of Ma-Schwede. We also prove that two-dimensional strongly $F$-regular singularities are stable under equal characteristic deformations. Our results give an affirmative answer to a conjecture of Liedtke-Martin-Matsumoto on deformations of linearly reductive quotient singularities. Comment: 31pages; v2: minor changes, Section 5 of v1 removed and incorporated into another paper |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2103.03721 |
| رقم الانضمام: | edsarx.2103.03721 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |