Weil空间与Weil-李群

摘要：

我们定义了任意交换基环K（特别是整数环）上的Weil空间、Weil流形、Weil簇和Weil李群，并发展了这种空间的基本理论，引出了附在Weil李群上的李代数的定义。根据定义，Weil空间的范畴是从K-Weil代数到集合的函子的范畴;因此，我们的Weil空间的概念类似于，但弱于E. Dubuc（1979）.鉴于A. Souvay，这种普遍性是适当的背景下制定和证明一般结果的无穷小微分几何，开始的方法开发的伯特伦，Mem. AMS 900。

英文摘要：

We define Weil spaces, Weil manifolds, Weil varieties and Weil Lie groups over an arbitrary commutative base ring K (in particular, over discrete rings such as the integers), and we develop the basic theory of such spaces, leading up the definition of a Lie algebra attached to a Weil Lie group. By definition, the category of Weil spaces is the category of functors from K-Weil algebras to sets; thus our notion of Weil space is similar to, but weaker than the one of Weil topos defined by E. Dubuc (1979). In view of recent result on Weil functors for manifolds over general topological base fields or rings by A. Souvay, this generality is the suitable context to formulate and to prove general results of infinitesimal differential geometry, as started by the approach developed in Bertram, Mem. AMS 900.

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