2012/01/22 by Sabine Lechner, Lechner, Sabine
Computer Science · Mathematics · #17B56 #57T10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Group Theory (math.GR) #Number Theory (math.NT) #Rings and Algebras (math.RA) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1201.4550
openalex publication_date 2012/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result of this work is a new proof and generalization of Lazard's comparison theorem of locally analytic group cohomology with Lie algebra cohomology for K-Lie groups, where K is a finite extension of the p-adic numbers. We show the following theorem: Let K be a finite extension of the p-adic numbers and let G be a K-Lie group. Then there exists an open subgroup U of G such that the Lazard morphism, which is induced by differentiating cochains, is an isomorphism. The proof of this theorem is independent of the proof of Lazard's comparison result. Our strategy to prove the comparison isomorphism between locally analytic group cohomology and Lie algebra cohomology uses the theory of formal group laws. And in a second step we consider standard groups.