Combinatorial Differential Forms

Details Combinatorial Differential Forms Combinatorial Differential Forms

2000-05-09

arxiv.org/abs/math/0005087v1

Mathematics

Algebraic Geometry

LaTeX, 49 pages, uses xy-Pic

Scientific paper

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.

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