| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
For the past decade, we have had a great interest in the number of rational points of a variety over a finite field. This project is also concerned with such a topic. The main result of this research project is as follows.
Let X be a hyper-surface of degree d in n-space over a finite field F of q-elements. We obtained a bound for the number of F-rational points of X. This bound is depending only on d, q and n, and also linear in d. We named this bound elementary bound. Moreover, for each (q, n), there are three hyper-surfaces with different degrees each other that attain the elementary bound. Additionally, we have determined the all surfaces in 3-space that attain the elementary bound.
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