2013 Fiscal Year Final Research Report
Multifaceted applications of rigid geometry to algebraic geometry
| Project/Area Number |
23540015
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kumamoto University |
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Principal Investigator |
KATO Fumiharu 熊本大学, 自然科学研究科, 教授 (50294880)
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| Project Period (FY) |
2011 – 2013
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| Keywords | リジッド幾何学 / 非アルキメデス的幾何学 |
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| Research Abstract |
The outcomes of the present research project is two-fold:
(1) Construction high-dimensional non-archimedean orbifolds via rigid analytic uniformizations: This part of the research has mainly been conducted by the joint-work with Daniel Allcock, University of Texas in Austin. Based on the past researches in this field, we have succeeded to give an explicit and algebro-geometrically significant algebraic surface that comes from 2-adic non-archimedean uniformization process.
(2) Building up the solid foundations of rigid geometry: This has been promised in the initial research proposal of this project, meant to be one of the main things to do in the second and third years. This part of the research saw a very successful achievement; with Kazuhiro Fujiwara (Nagoya), we have finished a foundational book `Foundations of Rigid Geometry', containing more than 700 pages, which has been accepted to be published from European Mathematical Society, Publishing House.
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