| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We characterized the Zariski-Riemann space (which is treated in Algebraic geometry) as an analog of Stone-Cech compactification, which is treated in Topology. We also re-defined proper morphisms to reach this goal. Also, we succeeded in formularizing convex geometry in pure algebraic manner; this means that there exists an algebraic type \tau such that convex polytopes can be regarded as a \tau-algebra. Furthermore, applying this technique to arithmetics, we succeeded in formularizing arithmetic compactification of the spectrum of algebraic integer ring in a pure-algebraic manner. This is accomplished by considering the above \tau-algebras and the construction of the Zariski-Riemann space simultaneously.
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