Combinatorial Differential Forms

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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.
LaTeX, 49 pages, uses xy-Pic

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Algebraic Geometry, Differential Geometry, 14B10; 14F40; 51K10; 58A10

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http://salesiana.dossiersoluciones.com/handle/123456789/59156

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0005087
 http://arxiv.org/abs/math/0005087

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arXiv