2017 Fiscal Year Final Research Report
Motive theory and algebraic cycles based on Weil reciprocity
| Project/Area Number |
15K04773
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Tohoku University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2015-04-01 – 2018-03-31
|
| Keywords | 代数学 / 数論幾何 / 代数幾何学 / 整数論 |
|---|
| 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.
|
| Free Research Field |
数論幾何
|
