Motive theory and algebraic cycles based on Weil reciprocity
Project/Area Number |
15K04773
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Tohoku University |
Principal Investigator |
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Project Period (FY) |
2015-04-01 – 2018-03-31
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Project Status |
Completed (Fiscal Year 2017)
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Budget Amount *help |
¥5,850,000 (Direct Cost: ¥4,500,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
|
Keywords | 代数学 / 数論幾何 / 代数幾何学 / 整数論 / モチーフ / 代数幾何 |
Outline of Final Research Achievements |
A triangulated category of motives with modulus is constructed in such a way that it enables us to handle non-homotopy invariant phenomena. This is a generalization of Voevodsky's triangulated category of motives. Our category has intimate relationship with reciprocity sheaves that was introduced in our previous work. We also studied the mixed Hodge structures with modulus, which is a counter-part of motives with modulus in the Hodge theory. We proved that the Nori category arising from curves with modulus is equivalent to Laumon 1-motives. This is an extension of a result of Ayoub and Barbieri-Viale that considers the case without modulus.
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Report
(4 results)
Research Products
(25 results)
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[Journal Article] Reciprocity sheaves2016
Author(s)
Bruno Kahn, Shuji Saito, Takao Yamazaki, Kay Ruelling
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Journal Title
Compositio Mathematica
Volume: 152
Issue: 9
Pages: 1851-1898
DOI
Related Report
Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
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[Presentation] Motives with modulus2016
Author(s)
Takao Yamazaki
Organizer
Algebraic K-theory and Motivic Cohomology
Place of Presentation
Mathematisches Forschungsinstitut Oberwolfach, ドイツ
Year and Date
2016-06-29
Related Report
Int'l Joint Research / Invited
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