Full paper in PDF:
$% M. Coste, J. M. Ruiz, and M. Shiota, Global problems on Nash functions,
Rev. Mat. Complut. 17 (2004), 83–115.%$
Global Problems on Nash Functions
IRMAR (UMR CNRS 6625)
Université de Rennes I, |
Departamento de Geometría y Topología,
Facultad de Matemáticas, |
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.
Key words: Nash function, étale morphism, cohomology, Cartan’s theorems A and B,
finite sheaf, semialgebraic topology, approximation theorem, real spectrum.
2000 Mathematics Subject Classification:
14P20, 32C07.