全纯D-模的中度与快速衰减邻近循环
Moderate and rapid-decay nearby cycles for holonomic D-modules
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中文总结 AI 辅助
针对全纯D-模引入与全纯函数相关的中度、快速衰减邻近循环概念，证明其为特殊纤维与圆周乘积上的ℝ-可构造复形，验证对偶性质并明确其与非正则复形的关系，论证主要依托Mochizuki的相关成果。
中文摘要 AI 辅助
我们针对任意全纯$\u27e8D\u27e9$-模，引入了与全纯函数$f$相关的中度与快速衰减邻近循环的概念。经证明，它们是定义在该函数的特殊纤维与以$f/|f|$取值为参数的圆周$S^1$的乘积上的$\u211d$-可构造复形。B. Hepler与A. Hohl[HH25]证明了其对偶性质，我们也在特殊情形下证明了这些性质。本文还给出了它们与Z. Mebkhout所定义的非正则复形之间的关系，大部分论证依托于T. Mochizuki[Moc14]的研究成果。
英文摘要
We introduce the notion of moderate and rapid decay nearby cycles relative to a holomorphic function $f$ for an arbitrary holonomic $\mathcal{D}$-module. They are proved to be $\mathbb{R}$-constructible complexes on the product of the special fiber of the function and the circle $S^1$ parametrizing the values of $f/|f|$. Duality properties are proved by B.\,Hepler and A.\,Hohl [HH25], and we also prove them in special cases. Relations with the irregularity complexes as defined by Z.\,Mebkhout are given. Most of the arguments rely on the results of T.\,Mochizuki [Moc14].
