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.
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Notes
- 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
S. Bosch, Algebraic Geometry and Commutative Algebra. Universitext (Springer, London, 2013)
S. Bosch, U. G”untzer, R. Remmert, Non-Archimedean Analysis. Grundlehren, Bd. 261 (Springer, Heidelberg, 1984)
N. Bourbaki, Algèbre Commutative, Chap. I–IV (Masson, Paris, 1985)
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)
A. Grothendieck, J.A. Dieudonné, Éléments de Géométrie Algébrique I. Grundlehren, Bd. 166 (Springer, Heidelberg, 1971)
A. Grothendieck, J.A. Dieudonné, Éléments de Géométrie Algébrique II. Publ. Math. 8 (1961)
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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DOI: https://doi.org/10.1007/978-3-319-04417-0_8
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