Title: Formal Manifold Structures on Positive Characteristic Varieties Show Chinese title

Title: 正特征流形结构的代数簇

Abstract: In his 1970 ICM report, Sullivan proposes the program of l-adic formalization of the concept of manifolds. In this program, he claims that smooth positive characteristic varieties should carry l-adic formal manifold structures. He also claims the existence of an abelianized Galois symmetry on l-adic formal manifold structures. This paper carries out this program, establishes the claims for certain varieties, and relates the abelianized Galois symmetry on l-adic formal manifold structures to the Galois symmetry of varieties. Meanwhile, we prove that a simply-connected variety is l-adic homotopic equivalent to a simply-connected finite CW complex if and only if the l-profinite completion of its etale homotopy type admits an l-local lifting. Show Chinese abstract

Abstract: 在他的1970年国际数学家大会报告中，Sullivan提出了流形概念的l-进形式化计划。 在这个计划中，他声称具有正特征的代数簇应该携带l-进形式流形结构。 他还声称在l-进形式流形结构上存在一个阿贝尔化的伽罗瓦对称性。 本文执行了这个计划，为某些代数簇建立了这些声明，并将l-进形式流形结构上的阿贝尔化伽罗瓦对称性与代数簇的伽罗瓦对称性联系起来。 同时，我们证明了一个单连通的代数簇与一个单连通的有限CW复形l-进同伦等价，当且仅当其etale同伦类型的l-有限陪域 admits 一个l-局部提升。