Cohomology of algebraic varieties and Galois representations
| Project/Area Number |
22244001
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
SAITO Takeshi 東京大学, 数理(科)学研究科(研究院), 教授 (70201506)
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| Co-Investigator(Kenkyū-buntansha) |
TAMAGAWA Akio 京都大学, 数理解析研究所, 教授 (00243105)
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| Co-Investigator(Renkei-kenkyūsha) |
TAGUCHI Yuichiro 九州大学, 数理学研究院, 准教授 (90231399)
TSUZUKI Nobuo 東北大学, 理学研究科, 教授 (10253048)
TSUJI Takeshi 東京大学, 大学院数理科学研究科, 教授 (40252530)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥19,370,000 (Direct Cost: ¥14,900,000、Indirect Cost: ¥4,470,000)
Fiscal Year 2013: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2012: ¥6,890,000 (Direct Cost: ¥5,300,000、Indirect Cost: ¥1,590,000)
Fiscal Year 2011: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2010: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
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| Keywords | 数論幾何学 / 分岐理論 / l進層 / 特性サイクル / ガロワ表現 / 代数学 / 整数論 / 代数幾何 / 代数多様体 / 分岐 / 特性輪体 / 隣接輪体 / 非輪状性 / ガロワ被覆 / 余接束 / エタール・コホモロジー / 超曲面 / 判別式 / 導手 / 局所体 / Stiefel-Whitney類 / 直交表現 |
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| Research Abstract |
I find that non-logarithmic version is geometrically more important than the logarithmic one in ramification theory. I constructed the non-logarithmic theory of the characteristic cycle of an l-adic sheaf in codimension at most 1. Using the method of cutting by curves and established acyclicity of morphisms of varieties.
For a sheaf on a surface, I defined the characteristic cycle everywhere on the surface and proved a formula for the Euler number and an analog of the Milnor formula on vanishing cycles. Though limited to surfaces, this is a significant result achieving the aim to construct a theory of characteristic cycles in higher dimension.
I also studied the determinant and the second Stiefel-Whitney class of the Galois representation defined by l-adic cohomology of a variety of even dimension.
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Report
(5 results)
Research Products
(58 results)
