The Langlands setup in the context of motivic homotopy theory.

2016 Fiscal Year Final Research Report

• 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
• Keywords: ラングランズ対応 / ガロア圏 / オペラッド

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.

Free Research Field

数論幾何学