
Journal of Lie Theory 27 (2017), No. 4, 915941 Copyright Heldermann Verlag 2017 Primary Spectrum of C^{∞}(M) and Jet Theory Ricardo J. AlonsoBlanco Department of Mathematics, University of Salamanca, Plaza de la Merced 14, 37004 Salamanca, Spain ricardo@usal.es Jesús MuñozDíaz Department of Mathematics, University of Salamanca, Plaza de la Merced 14, 37004 Salamanca, Spain clint@usal.es We consider, for each smooth manifold M, the set M of all primary ideals of C^{∞}(M) which are closed and whose radical is maximal. The classical Lie theory of jets (jets of submanifolds) must be extended to M in order to have nice functorial properties. We will begin with the purely algebraic notions, referred always to the ring C^{∞}(M). Subsequently, the differentiable structures on each jet space of a given type will be introduced. The theory of contact systems, which generalizes the classical one, has a purely algebraic part and another one which depends on the differentiable structures. Keywords: Jets, primary ideals, rings of functions, spectrum, contact system. MSC: 58A20 [ Fulltextpdf (250 KB)] for subscribers only. 