Real Algebraic and Analytic Geometry

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20. Michel Coste, Jesús M. Ruiz, Masahiro Shiota:
Global Problems on Nash Functions.

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Submission: 2002, October 25.

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.

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