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Raynaud’s View on Rigid Spaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2105)

Abstract

This chapter contains Raynaud’s characterization of rigid spaces in terms of formal scheme models. As an important technical tool admissible formal blowing-up is needed, which is explained in detail.

Keywords

  • Rigid Spacer
  • Formal Scheme Models
  • Admissible Covering
  • Affine Open Part
  • Complete Valuation Ring

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

    Beyond the classical rigid case, the notion of rig-points is useful when R is a general adic ring of type (V) or (N). Such rig-points will not necessarily be closed, as is the case in classical rigid geometry; cf. Lemma 3 below.

References

  1. S. Bosch, Algebraic Geometry and Commutative Algebra. Universitext (Springer, London, 2013)

    Google Scholar 

  2. S. Bosch, U. G”untzer, R. Remmert, Non-Archimedean Analysis. Grundlehren, Bd. 261 (Springer, Heidelberg, 1984)

    Google Scholar 

  3. N. Bourbaki, Algèbre Commutative, Chap. I–IV (Masson, Paris, 1985)

    Google Scholar 

  4. B. Conrad, Deligne’s notes on Nagata compactifications. J. Ramanujan Math. Soc. 22, 205–257 (2007); Erratum. J. Ramanujan Math. Soc. 24, 427–428 (2009)

    Google Scholar 

  5. A. Grothendieck, J.A. Dieudonné, Éléments de Géométrie Algébrique I. Grundlehren, Bd. 166 (Springer, Heidelberg, 1971)

    Google Scholar 

  6. A. Grothendieck, J.A. Dieudonné, Éléments de Géométrie Algébrique II. Publ. Math. 8 (1961)

    Google Scholar 

  7. A. Grothendieck, J.A. Dieudonné, Éléments de Géométrie Algébrique III. Publ. Math. 11, 17 (1961/1963)

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Bosch, S. (2014). Raynaud’s View on Rigid Spaces. In: Lectures on Formal and Rigid Geometry. Lecture Notes in Mathematics, vol 2105. Springer, Cham. https://doi.org/10.1007/978-3-319-04417-0_8

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