On global Nash functions

Jesús M. Ruiz; Masahiro Shiota

Displaying similar documents to “On global Nash functions”

Global problems on Nash functions.

Michel Coste, Jesús M. Ruiz, Masahiro Shiota (2004)

Revista Matemática Complutense

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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.

Separation, factorization and finite sheaves on Nash manifolds

Michel Coste, Jesús M. Ruiz, Masahiro Shiota (1996)

Compositio Mathematica

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Algebraic approximation of structures over complete local rings

Michael F. Artin (1969)

Publications Mathématiques de l'IHÉS

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On the pythagoras numbers of real analytic surfaces

Francesca Acquistapace, Fabrizio Broglia, José F. Fernando, Jesús M. Ruiz (2005)

Annales scientifiques de l'École Normale Supérieure

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Analytic cell decomposition and analytic motivic integration

Raf Cluckers, Leonard Lipshitz, Zachary Robinson (2006)

Annales scientifiques de l'École Normale Supérieure

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Irreducible components of rigid spaces

Brian Conrad (1999)

Annales de l'institut Fourier

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This paper lays the foundations for the global theory of irreducible components of rigid analytic spaces over a complete field $k$ . We prove the excellence of the local rings on rigid spaces over $k$ . This is used to prove the standard existence theorems and to show compatibility with the notion of irreducible components for schemes and formal schemes. Behavior with respect to extension of the base field is also studied. It is often necessary to augment scheme-theoretic techniques with other...