2003 Fiscal Year Final Research Report Summary
Research on duality theorems of modules on fans
| Project/Area Number |
12640006
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Tohoku University |
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Principal Investigator |
ISHIDA Masanori Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30124548)
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| Co-Investigator(Kenkyū-buntansha) |
KAJIWARA Takeshi Tohoku University, Graduate School of Science, Research Assistant, 大学院・理学研究科, 助手 (00250663)
ITO Hiroyuki Hiroshima University, Graduate School of engineering, Associate Professor, 大学院・工学研究科, 助教授 (60232469)
HARA Nobuo Tohoku University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90298167)
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| Project Period (FY) |
2000 – 2003
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| Keywords | algebraic variety / toric variety / abelian variety / elliptic curve / blowup / Rees alebra / fan |
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| Research Abstract |
Ishida studied on not necessarily rational fan as a generalization of the theory of toric varieties. He constructed the theory of Zariski-Riemann spaces of fans.
Hara defined the tight closure of ideals associated with a fixed ideals as a generalization of the theory of tight closures of ideals.
Ito studied on the Mordell-Weil lattices of elliptic curves from the view point of singularity theory and deformation theory.
Kajiwara studied on the Deligne conjecture on the l-adic etale cohomology of nonsingular algebraic varieties defined over a valuation ring.
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