论文标题
Steenbrink同构和管状社区的晶体
Steenbrink isomorphism and crystals on tubular neighbourhoods
论文作者
论文摘要
对于在适当（严格的）在一个小的多盘上具有相对水平的简单正常越过除数的适当（严格）的可半固定家庭的局部尼尔疗法的连接，我们在派生类别中构建了一个规范的部分 起源。作为本节存在的应用，我们证明了以下内容：（1）：通过纯粹的代数方法，较高直接图像的本地烦恼； （2）：在log de rham的基本变化对数纤维的基本变化与上面的较高直接图像之间的基本变化之间存在规范同构。结果（2）告诉我们，较高的直接图像具有结晶性质：较高直接图像的不变性。
For a locally nilpotent integrable connection on a proper (strict) semistable family over a small polydisc with a relative horizontal simple normal crossing divisor, we construct a canonical section in derived categories inducing an isomorphism from the log de Rham cohomology of it on the log special fiber of this family to the stalk of the higher direct image of it at the origin modulo the maximal ideal of the localization of the structure sheaf at the origin. As an application of the existence of this section, we prove the following: (1): the locally freeness of the higher direct image by a purely algebraic method; (2): the existence of a canonical isomorphism between the base change of the log de Rham cohomology of the log special fiber to the small polydisc and the higher direct image above. The result (2) tells us that the higher direct image has the crystalline nature: the invariance of the higher direct image.
