2017 Fiscal Year Final Research Report
Study on unramified cohomology and algebraic surfaces over arithmetic fields of higher dimension
| Project/Area Number |
15K17526
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Meijo University (2017)
National Institute of Technology, Toyota College (2015-2016) |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | Brauer 群 / 不分岐コホモロジー / 対角的2次曲面 / 対角的3次曲線 / 対角的3次曲面 / 生成元 |
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| Outline of Final Research Achievements |
In this research, we studied unramified cohomology of varieties defined by diagonal equations. In particular, for the second unramified cohomology, that is, the Brauer group, we obtained the following results.
1. We found that there does not exist a uniform generator of the Brauer group for a general 3-parametrized family of affine diagonal quadrics.
2. For Fermat curves of degree three, a particular case of diagonal cubic curves, we found an explicit symbolic generator of the 3-torsion part of their Brauer groups.
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| Free Research Field |
代数学
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