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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 45634 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Rastegar, Arash
- Abstract:
- Rigid analytic geometry was developed by John Tate in 1971. Although it seems that a rigid analytic spaces on non-Archimedean field F, is like something called F-analytic manifold; however in general these two are distinct concepts.
In this thesis; we introduce rigid analytic spaces. It begins in chapter one by non-Archimedean fields. In this chapter also contains theorem 1-3-7; which there is no proof for it without usage of methods of this chapter; up to the present. Topics discussed in this chapter are interesting subjects of other applica¬tions of non-Archimedean fields. There is a visualization of the field Q_p; and an appendix includes some definitions and consequences of ordered rings to detoxify ambiguity.
Second chapter contains concept of affinoid spaces (which are locally rigid analytic spaces). Theorem 2-2-10 in this chapter expresses an interesting applic¬ation of norms on affinoid algebras.
Chapter three is dedicated to some of Grothendieck topology and sheaf theory and defines concept of rigid analytic spaces and gives some standard exa¬mples of rigid spaces.
The first three chapters developed so that reader can comprehend them without information about algebraic geometry.
Finally; chapter four; which have more analysis and geometry instead of algebra; developed to reach p-adic version of the Poincare theorem mentioned in theorem 4-5-7.
- Keywords:
- Affinoid Spaces ; Affinoid Morphism ; Grothendieck Topology ; Ringed Spases ; Rigid Spaces ; Bidisk ; Bianalytic Maps
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