This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetherianness. We discuss all of them in the various possible contexts, from manifolds over the reals to real spectra of arbitrary commutative rings.
@article{urn:eudml:doc:44533,
title = {Global problems on Nash functions.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {17},
year = {2004},
pages = {83-115},
zbl = {1056.14081},
mrnumber = {MR2063943},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44533}
}
Coste, Michel; Ruiz, Jesús M.; Shiota, Masahiro. Global problems on Nash functions.. Revista Matemática de la Universidad Complutense de Madrid, Tome 17 (2004) pp. 83-115. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44533/