Irreducible components of rigid spaces

Brian Conrad

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 2, page 473-541
  • ISSN: 0373-0956

Abstract

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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 algebraic and geometric arguments.

How to cite

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Conrad, Brian. "Irreducible components of rigid spaces." Annales de l'institut Fourier 49.2 (1999): 473-541. <http://eudml.org/doc/75345>.

@article{Conrad1999,
abstract = {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.},
author = {Conrad, Brian},
journal = {Annales de l'institut Fourier},
keywords = {irreducible component; rigid analysis; excellence; Fredholm series},
language = {eng},
number = {2},
pages = {473-541},
publisher = {Association des Annales de l'Institut Fourier},
title = {Irreducible components of rigid spaces},
url = {http://eudml.org/doc/75345},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Conrad, Brian
TI - Irreducible components of rigid spaces
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 2
SP - 473
EP - 541
AB - 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.
LA - eng
KW - irreducible component; rigid analysis; excellence; Fredholm series
UR - http://eudml.org/doc/75345
ER -

References

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