GROUP COVERS, o-MINIMALITY, AND CATEGORICITY

Q4 Mathematics

Confluentes Mathematici Pub Date : 2010-09-26 DOI:10.1142/S1793744210000259

A. Berarducci, Y. Peterzil, A. Pillay

引用次数: 6

Abstract

We study the model theory of "covers" of groups H definable in an o-minimal structure M. We pose the question of whether any finite central extension G of H is interpretable in M, proving some cases (such as when H is abelian) as well as stating various equivalences. When M is an o-minimal expansion of the reals (so H is a definable Lie group) this is related to Milnor's conjecture [15], and many cases are known. We also prove a strong relative Lω1, ω-categoricity theorem for universal covers of definable Lie groups, and point out some notable differences with the case of covers of complex algebraic groups (studied by Zilber and his students).

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组覆盖，极小性和分类性

我们研究了群H在0 -极小结构M中可定义的“覆盖”的模型理论。我们提出了H的有限中心扩展G在M中是否可解释的问题，证明了一些情况(如H是阿贝尔的)，并陈述了各种等价。当M是实数的o极小展开式(H是可定义李群)时，这与Milnor的猜想有关[15]，许多情况是已知的。我们还证明了可定义李群的泛覆盖的一个强相对Lω1， ω-范畴定理，并指出了与复代数群的覆盖情况(由Zilber和他的学生研究)的一些显著区别。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.