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Adic Rings and Their Associated Formal Schemes

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

Abstract

Similarly as in arithmetic algebraic geometry, there is the notion of formal scheme models for rigid spaces. The theory of formal schemes is developed from scratch and basic properties are established.

Keywords

  • Prime Ideal
  • Finite Type
  • Formal Scheme
  • Valuation Ring
  • Projective Limit

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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References

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

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

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

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  4. M. Raynaud, L. Gruson, Critères de platitude et de projectivité. Invent. Math. 13, 1–89 (1971)

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© 2014 Springer International Publishing Switzerland

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Bosch, S. (2014). Adic Rings and Their Associated Formal Schemes. 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_7

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