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.
Classification :
58A20
Mots-clés :
Jets, primary ideals, rings of functions, spectrum, contact system
Affiliations des auteurs :
Ricardo J. Alonso-Blanco
1
;
Jesús Muñoz-Díaz
1
1
Department of Mathematics, University of Salamanca, Plaza de la Merced 1-4, 37004 Salamanca, Spain
Ricardo J. Alonso-Blanco; Jesús Muñoz-Díaz. Primary Spectrum of C∞(M) and Jet Theory. Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 915-941. http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a1/
@article{JOLT_2017_27_4_a1,
author = {Ricardo J. Alonso-Blanco and Jes\'us 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a1/}
}
TY - JOUR
AU - Ricardo J. Alonso-Blanco
AU - Jesús Muñoz-Díaz
TI - Primary Spectrum of C∞(M) and Jet Theory
JO - Journal of Lie Theory
PY - 2017
SP - 915
EP - 941
VL - 27
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a1/
ID - JOLT_2017_27_4_a1
ER -
%0 Journal Article
%A Ricardo J. Alonso-Blanco
%A Jesús Muñoz-Díaz
%T Primary Spectrum of C∞(M) and Jet Theory
%J Journal of Lie Theory
%D 2017
%P 915-941
%V 27
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a1/
%F JOLT_2017_27_4_a1
