2014/02/11 by Wolfgang Bertram, Bertram, Wolfgang
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.CT #math.GR
paper · pdf · doi:10.48550/arxiv.1402.2619
arxiv created 2014/02/11 · openalex publication_date 2014/02/11 · arxiv updated 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.