The Langlands setup in the context of motivic homotopy theory.
Project/Area Number |
25800005
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | The University of Tokyo |
Principal Investigator |
Kondo Satoshi 東京大学, カブリ数物連携宇宙研究機構, 客員准科学研究員 (30372577)
|
Project Period (FY) |
2013-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | ラングランズ対応 / ガロア圏 / オペラッド / リヒテンバウム予想 / 代数曲線のモジュライ / オペラッド構造 / モジュラーシンボル / 代数ホモトピー / モチーフ / 代数曲線 |
Outline of Final Research Achievements |
The aim was to understand better the Langlands correspondence using motivic homotopy theory. From the topological point of view, we constructed a structure called modular operad (concerning the composition law) on the moduli of embeddings of pointed curves. Concerning the automorphic representation theory, we gave certain axioms on sites such that when they are met, the topos is equivalent to the category of representations of some locally profinite groups. The motivations of the two results above are related to motivic homotopy theory, but there is no direct technical relation. We did not obtain an application to the Beilinson conjectures.
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Report
(5 results)
Research Products
(18 results)