局部有限 pro-有限环

局部紧致集上层上同调的计算技术

Computational techniques for sheaf cohomology of locally profinite sets

本文提出k-sheer划分用于计算局部紧致集上常系数Z_2的上同调，通过非平凡顶上同调元作为coboundaries的极限，将中间上同调问题转化为顶上同调问题。

关于局部紧致集的上同调

On cohomology of locally profinite sets

本文在Zermelo-Fraenkel集合论中构造了首个非递降且忠实平坦的交换环之间映射的例子，涉及局部紧致集的上同调结构。

Profinite algebras and affine boundedness

We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a topological algebra, whereas for topological groups, rings, semigroups, and distributive lattices, profiniteness turns out to be a purely topological property as it is is equivalent to the underlying topological space being a Stone space. Condensing the core idea of those classical results, we introduce the concept of affine boundedness for an arbitrary unive…

Geometric stability theory for $μ$-structures

We introduce a notion of $μ$-structures which are certain locally compact group actions and prove some counterparts of results on Polish structures(introduced by Krupinski in \cite{Kru5}). Using the Haar measure of locally compact groups, we introduce an independence, called $μ$-independence, in $μ$-structures having good properties. With this independence notion, we develop geometric stability theory for $μ$-structures. Then we see some structural theorems for compact groups which are $μ$-structure. We also give examples of profinite structures where $μ$-independence is different from $nm$-in…

类型较少的域和环

Fields and rings with few types

设R是具有可能额外结构的结合环。称R是弱小的，如果在R的任何有限子集上有可数多个1-型。它是局部P，如果R的任何有限子集的代数闭包具有性质P。本文证明了弱小域的有限次域扩张要么是有限域，要么没有Artin-Schreier扩张。特征为2的弱小域是有限的或代数闭的。每个正特征的弱小除环在其中心上是局部有限维的。弱小环的Jacobson根是局部幂零的。每一个弱小除环局部模其Jacobson根同构于除环上的n个矩阵环的乘积。