Abstract
In this chapter we establish two important theorems: the Theorem of Gerritzen–Grauert on the structure of affinoid subdomains and the Acyclicity Theorem of Tate. Both results are fundamental for setting up rigid geometry.
Keywords
- Rational Covering
- Residue Class
- Common Zero
- Finite Covering
- Unit Ideal
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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)
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Bosch, S. (2014). Affinoid Functions. 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_4
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DOI: https://doi.org/10.1007/978-3-319-04417-0_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04416-3
Online ISBN: 978-3-319-04417-0
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