Motive theory based on Weil reciprocity
Project/Area Number |
24654001
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
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Research Institution | Tohoku University |
Principal Investigator |
YAMAZAKI Takao 東北大学, 理学(系)研究科(研究院), 教授 (00312794)
|
Project Period (FY) |
2012-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 数論幾何 / モチーフ / 代数学 / 代数的サイクル / 国際研究者交流(フランス) / Weil 相互律 |
Outline of Final Research Achievements |
Celebrated theory of mixed motives, due to Voevodsky, is yet to be extended in order to take into account non-homotopy invariant objects. Indeed, there are fundamental objects, such as relative Picard group of an algebraic curve, that are not homotopy invariant. By taking Weil reciprocity in the place of homotopy invariance, we established a theory of `reciprocity presheaves', which is expected to become a foundation for an extended motive theory encompassing non-homotopy invariant objects.
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Report
(4 results)
Research Products
(18 results)