2000/05/09 by Lawrence Breen, Breen, Lawrence, William Messing +1 · 1 citation
Mathematics · Physics and Astronomy · #14B10 #14F40 #51K10 #58A10 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.AG #math.DG #msc:14B10 #msc:14F40 #msc:51K10 #msc:58A10
paper · pdf · doi:10.48550/arxiv.math/0005087
LaTeX, 49 pages, uses xy-Pic
arxiv created 2000/05/09 · openalex publication_date 2000/05/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend to a scheme-theoretic context the notion of a combinatorial differential form, due to A.Kock in the framework of synthetic differential geometry. We show that group-valued combinatorial forms on a scheme may be identified, under very general hypotheses, with traditional Lie algebra-valued differential forms, and that their Lie algebra structure can be recovered from first principles. Some basic results from differential geometry (Maurer-Cartan equation, Bianchi identity), as well as a higher analogue, are obtained by exploiting this identification.