Algebraic curves over finite fields and their applications to coding theory and finite geometry
| Project/Area Number |
24540056
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kanagawa University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2012-04-01 – 2016-03-31
|
| Project Status |
Completed (Fiscal Year 2015)
|
| 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)
|
|---|
| Keywords | 代数多様体 / 有限体 / 射影空間 / 超曲面 / 射影代数幾何 / 代数曲面 / 平面曲線 / 国際情報交換（韓国） / 代数学 / 代数幾何学 / 有限幾何 / 符号理論 / 国際研究者交流 韓国，ブラジル / 代数曲線 / 「国際情報交換」韓国，アメリカ合衆国 / 「国際研究者交流」ブラジル |
|---|
| 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.
|
Report
(5 results)
Research Products
(14 results)
