Research of arithmetic fundamental groups of hyperbolic curves
Project/Area Number |
20740010
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Algebra
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Research Institution | Kyoto University |
Principal Investigator |
HOSHI Yuichiro Kyoto University, 数理解析研究所, 助教 (50456761)
|
Project Period (FY) |
2008 – 2009
|
Project Status |
Completed (Fiscal Year 2009)
|
Budget Amount *help |
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
Keywords | 遠アーベル幾何 / 数論的基本群 / 双曲的曲線 / 配置空間 / 外Galois表現 / 組み合わせ論的カスプ化 / モノドロミー充満 / Galois切断 / 副p切断予想 / tame-blind / truncated Barsotti-Tate群 / 組み合わせ論版Grothendieck予想 |
Research Abstract |
By a joint work with Shinichi Mochizuki, we proved the injectivity portion of the combinatorial cuspidalization; moreover, as an arithmetic application of this injectivity, we obtained the faithfulness of the outer Galois representations associated to hyperbolic curves over number or p-adic local fields. Next, I introduced the notion of monodromic fullness for hyperbolic curves and proved an anabelian conjecture-type result for certain monodromically full hyperbolic curves of genus zero. Finally, I proved that in general, the pro-p section conjecture for hyperbolic curves over number fields, as well as p-adic local fields, cannot be resolved in the affirmative.
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Report
(3 results)
Research Products
(16 results)