Journal of Lie Theory

no. 4
Primary Spectrum of C∞(M) and Jet Theory
Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 915-941
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.
DOI: 10.5802/jolt.975
Classification: 58A20
Keywords: Jets, primary ideals, rings of functions, spectrum, contact system 
@article{JOLT_2017_27_4_a1,
     author = {R. J. Alonso-Blanco and J. Mu\~noz-D{\'\i}az},
     title = {Primary {Spectrum} of {C\protect\textsuperscript{\ensuremath{\infty}}(M)} and {Jet} {Theory}},
     journal = {Journal of Lie Theory},
     pages = {915--941},
     year = {2017},
     volume = {27},
     number = {4},
     doi = {10.5802/jolt.975},
     zbl = {1395.58003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.975/}
}
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R. J. Alonso-Blanco; J. Muñoz-Díaz. Primary Spectrum of C∞(M) and Jet Theory. Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 915-941. doi: 10.5802/jolt.975

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