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.
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References
M. Artin, Grothendieck Topologies. Notes on a Seminar by M. Artin, Harvard University, Cambridge, 1962
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)
N. Bourbaki, Espaces Vectoriels Topologiques, Chap. I (Hermann, Paris, 1953)
R. Godement, Théorie des Faisceaux (Herrmann, Paris, 1964)
A. Grothendieck, Sur quelques points d’algèbre homologique. Tôhoku Math. J. 9, 119–221 (1957)
A. Grothendieck, J.A. Dieudonné, Éléments de Géométrie Algébrique I. Grundlehren, Bd. 166 (Springer, Heidelberg, 1971)
R. Kiehl, Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie. Invent. Math. 2, 256–273 (1967)
R. Kiehl, Der Endlichkeitssatz f”ur eigentliche Abbildungen in der nichtarchimedischen Funktionentheorie. Invent. Math. 2, 191–214 (1967)
U. K”opf, ”Uber eigentliche Familien algebraischer Variet”aten ”uber affinoiden R”aumen. Schriftenr. Math. Inst. Univ. M”unster, 2. Serie, Heft 7 (1974)
W. L”utkebohmert, Formal-algebraic and rigid-analytic geometry. Math. Ann. 286, 341–371 (1990)
M. Temkin, On local properties of non-Archimedean analytic spaces. Math. Ann. 318, 585–607 (2000)
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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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DOI: https://doi.org/10.1007/978-3-319-04417-0_6
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