论文标题
消失的循环和微量定位之间的等效性
An equivalence between vanishing cycles and microlocalization
论文作者
论文摘要
我们使用在Arxiv中开发的准平滑爆炸理论来定义沿准平滑闭合沉浸式的专业化和微电脑化的函数：1802.05702 [Math.ag]。 我们的第一个主要结果描述了沿衍生的零纤维的包含作为一定功能的消失循环的整个微电位函数。证明是基于这样的观察结果，即整个傅立叶变换可以写成消失的周期。最近，塔苏基·金乔（Tasuki Kinjo）在arxiv中获得了略有不同的设置的等效结果：2109.06468 [Math.ag]使用不同的证明方法。 Our second main result is an equivalence between the canonical twisted vanishing cycles sheaf introduced by Brav, Bussi, Dupont, Joyce, Szendrői, and Schürmann on the $-1$-shifted cotangent bundle of a quasi-smooth scheme and the quasi-smooth microlocalization of the perverse constant sheaf.
We define the functors of specialization and microlocalization along a quasi-smooth closed immersion using the theory of quasi-smooth blow-ups developed in arXiv:1802.05702 [math.AG]. Our first main result describes the entire microlocalization functor along the inclusion of a derived zero fiber as the vanishing cycles with respect to a certain function. The proof is based on the observation that the entire Fourier-Sato transform may be written as a vanishing cycles. An equivalent result in a slightly different setting was recently obtained by Tasuki Kinjo in arXiv:2109.06468 [math.AG] using a different method of proof. Our second main result is an equivalence between the canonical twisted vanishing cycles sheaf introduced by Brav, Bussi, Dupont, Joyce, Szendrői, and Schürmann on the $-1$-shifted cotangent bundle of a quasi-smooth scheme and the quasi-smooth microlocalization of the perverse constant sheaf.
