Irreducible components of rigid spaces
Annales de l'Institut Fourier, Volume 49 (1999) no. 2, p. 473-541

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 algebraic and geometric arguments.

Cet article donne les fondements de la théorie globale des composantes irréductibles d’espaces analytiques rigides sur un corps complet k. Nous prouvons l’excellence d’anneaux locaux sur les espaces rigides sur k. De là, nous prouvons les théorèmes standard d’existence et nous montrons la compatibilité avec les notions des composantes irréductibles pour les schémas et les schémas formels. Le comportement par rapport à l’extension du corps de base est aussi étudié. Il est souvent nécessaire de compléter les techniques de la théorie des schémas par d’autres arguments algébriques et géométriques.

@article{AIF_1999__49_2_473_0,
     author = {Conrad, Brian},
     title = {Irreducible components of rigid spaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {2},
     year = {1999},
     pages = {473-541},
     doi = {10.5802/aif.1681},
     zbl = {0928.32011},
     mrnumber = {2001c:14045},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1999__49_2_473_0}
}
Conrad, Brian. Irreducible components of rigid spaces. Annales de l'Institut Fourier, Volume 49 (1999) no. 2, pp. 473-541. doi : 10.5802/aif.1681. http://www.numdam.org/item/AIF_1999__49_2_473_0/

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