Geometry of Moduli Spaces and Galois Actions
模空间的几何和伽罗瓦作用
基本信息
- 批准号:13440005
- 负责人:
- 金额:$ 4.67万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (B)
- 财政年份:2001
- 资助国家:日本
- 起止时间:2001 至 2003
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
We investigated arithmetic geometry using a nonabelian invariant, the fundamental group. Head investigator proved the following : the derivation Lie algebra of Galois action on the fundamental group of projective line minus three points is generated by the Soule elements. This solves the generation conjecture by Deligne and Ihara. The result was published in Compositio Mathematicae. Using a similar construction, Head investigator proved the following result on the action of the arithmetic fundamental group of the moduli space on the fundamental group of curves. The image of the action of the absolute Galois group on the unipotent fundamental group of a curve C is maximal, if and only if the algebraic cycle C-C^-in the Jacobian of C has non-torsion image by l-adic Abel Jacobi map in the Galois cohomology. The result is to appear in J. Inst. Math. Jussieu. Tamagawa researched the reconstruction of a curve in the positive characteristic case from its geometric fundamental groups. He proved that it is possible if genus is zero, and is possible up to finite isomorphic classes in a general case. The result was published in J. Alg. Geom. Mochizuki is generalizing the anabelian geometry which reconstructs a scheme from its etale fundamental group, and is constructing a theory of categorical arithmetic geometry, which is expected to have a good contribution to ABC conjecture. Tsuzuki established the descent theory of the rigid cohomology and prove the finiteness of its dimension and degeneration of the weight spectral sequences. The result is published in Rend. Sem. Mat. Univ Padova. Kimura defined the notion of finite dimensionality of pure motives using symmetric and exterior products, and proved them in the case of curves. S. Morita made a good advance towards Faber's conjecture on the cohomology ring of the moduli space. The result was published in Topology.
我们研究算术几何使用nonabel不变,基本组。主要研究者证明了:伽罗瓦作用在射影直线减三点的基本群上的导子李代数是由Soule元生成的。这解决了Deligne和Ihara的生成猜想。结果发表在Compositio Mathematicae上。使用类似的建设,负责调查证明了以下结果的行动算术基本组的模空间的基本组的曲线。绝对伽罗瓦群在曲线C的幂幺基本群上的作用象是极大的,当且仅当C的Jacobian中的代数圈C-C^-在伽罗瓦上同调中具有l-adic Abel Jacobi映射的非挠象。结果将出现在J. Inst. Math. Jussieu。玉川从曲线的几何基本群出发,研究了正特征曲线的重构问题。他证明,这是可能的,如果属是零,是可能的有限同构类在一般情况下。结果发表在J. Alg。Mochizuki推广了从其基本群重构概型的Anabel几何,并建立了范畴算术几何理论,有望对ABC猜想做出贡献。Tsuzuki建立了刚性上同调的下降理论,证明了其维数的有限性和权谱序列的退化性。结果发表在Rend上。Sem等Mat.帕多瓦大学。木村用对称和外积定义了纯动机的有限维概念,并在曲线的情况下证明了这一点。S.森田提出了一个很好的进展费伯猜想的上同调环的模空间。结果发表在Topology上。
项目成果
期刊论文数量(144)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
N.Tsuzuki: "On base change theorem and coherence in rigid cohomology"Documenta Math.Extra Volume Kazuya Kato's Fiftieth Birthday. Extra Volume. 891-918 (2003)
N.Tsuzuki:“论刚性上同调的基变定理和相干性”Documenta Math.Extra Volume Kazuya Kato 五十岁生日。
- DOI:
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- 影响因子:0
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- 通讯作者:
M.Kaneko: "On multiple L-values"J.Math.Soc.Japan. (to appea).
M.Kaneko:“论多个 L 值”J.Math.Soc.Japan。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
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N.Tsuzuki: "On base change theorem and coherence in rigid cohomology"Documenta Math.Extra Volume : Kazuya Kato's Fiftieth Birthday. 891-918 (2003)
N.Tsuzuki:“论刚性上同调的基变定理和相干性”Documenta Math.Extra Volume:Kazuya Kato 五十岁生日。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
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- 通讯作者:
A.Tamagawa: "Finiteness of isomorphism classes of curves in positive characteristic with prescribed fundamental groups"Journal of Algebraic Geometry. (発表予定).
A. Tamakawa:“具有规定基本群的正特征曲线的同构类的有限性”代数几何杂志(待出版)。
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- 影响因子:0
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Richard Hain, Makoto Matsumoto: "Tannakian fundamental groups associated to Galois groups"MSRI publications. (発表予定).
Richard Hain、Makoto Matsumoto:“与伽罗瓦群相关的坦纳克基本群”MSRI 出版物(待出版)。
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MATSUMOTO Makoto其他文献
MATSUMOTO Makoto的其他文献
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{{ truncateString('MATSUMOTO Makoto', 18)}}的其他基金
Number theory, geometry and their application to algorithm
数论、几何及其在算法中的应用
- 批准号:
18K03213 - 财政年份:2018
- 资助金额:
$ 4.67万 - 项目类别:
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IgE-mediated host defense mechanism during Strongyloides venezuelensisinfection
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22590384 - 财政年份:2010
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21654017 - 财政年份:2009
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New developments in number theory and geometry : arithmetic topology, categorical arithmetic geometry, algorithm
数论与几何新进展:算术拓扑、分类算术几何、算法
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19204002 - 财政年份:2007
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19590501 - 财政年份:2007
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Beyond the framework of classical arithmetic geometry-Zeta, arithmetic topology, and categorical arithmetic geometry
超越经典算术几何的框架——Zeta、算术拓扑和分类算术几何
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16204002 - 财政年份:2004
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A Clinical, Periodical and Physiological Evaluation of Changes in Masticatory Load Center and Function
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- 批准号:
08457653 - 财政年份:1997
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A Physiological Evaluation Hybrid Oral Rehabilitation
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05454527 - 财政年份:1993
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A Physiological and Morphological Evaluation for Designing of Bilateral Free End Saddle Denture Occlusion
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- 批准号:
01480445 - 财政年份:1989
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Theraptic occlusal function in geriatrically maturated partially edentate mouth by removable partial denture
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62480476 - 财政年份:1987
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Grant-in-Aid for General Scientific Research (B)