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Coherent Sheaves on Rigid Spaces

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

Abstract

In this chapter we study the cohomology of coherent modules on rigid spaces and give a proof of an advanced result of Kiehl, the Proper Mapping Theorem.

Keywords

  • Exact Sequence
  • Cohomology Group
  • Direct Image
  • Canonical Morphism
  • Injective Resolution

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. M. Artin, Grothendieck Topologies. Notes on a Seminar by M. Artin, Harvard University, Cambridge, 1962

    MATH  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. N. Bourbaki, Espaces Vectoriels Topologiques, Chap. I (Hermann, Paris, 1953)

    Google Scholar 

  5. R. Godement, Théorie des Faisceaux (Herrmann, Paris, 1964)

    Google Scholar 

  6. A. Grothendieck, Sur quelques points d’algèbre homologique. Tôhoku Math. J. 9, 119–221 (1957)

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  8. R. Kiehl, Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie. Invent. Math. 2, 256–273 (1967)

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. R. Kiehl, Der Endlichkeitssatz f”ur eigentliche Abbildungen in der nichtarchimedischen Funktionentheorie. Invent. Math. 2, 191–214 (1967)

    CrossRef  MATH  MathSciNet  Google Scholar 

  10. U. K”opf, ”Uber eigentliche Familien algebraischer Variet”aten ”uber affinoiden R”aumen. Schriftenr. Math. Inst. Univ. M”unster, 2. Serie, Heft 7 (1974)

    Google Scholar 

  11. W. L”utkebohmert, Formal-algebraic and rigid-analytic geometry. Math. Ann. 286, 341–371 (1990)

    Google Scholar 

  12. M. Temkin, On local properties of non-Archimedean analytic spaces. Math. Ann. 318, 585–607 (2000)

    CrossRef  MATH  MathSciNet  Google Scholar 

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Bosch, S. (2014). Coherent Sheaves 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_6

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