Coste, M.Ruiz Sancho, Jesús MaríaShiota, Masahiro2023-06-202023-06-2020041988-2807https://hdl.handle.net/20.500.14352/50596This 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.engjournal articlehttp://www.mat.ucm.es/serv/revmat/vol17-1d.htmlhttp://www.mat.ucm.esrestricted access512.7515.171.5Nash function: étale morphismcohomologyCartan’s theorems A and Bfinite sheafsemialgebraic topologyapproximation theoremreal spectrumGeometria algebraica1201.01 Geometría Algebraica