Work

On Euler systems for motives and Heegner points

Year: 2024

Type: article

Abstract: We formulate an Iwasawa main conjecture for a higher rank Euler system for a general motive. We prove “one half" of the main conjecture under mild hypotheses. We also formu- late a conjecture on “Darmon-type derivatives" of Euler systems and give an application to the Tamagawa number conjecture. Lastly, we specialize our general framework to the setting of Heegner points and give a natural interpretation of the Heegner point main conjecture in terms of rank two Euler systems.

Source: Journal of the Association for Mathematical Research.

DOI: 10.56994/jamr.002.002.001

Authors: Takenori Kataoka, Takamichi Sano

Institutions: Tokyo University of Science, Osaka Metropolitan University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Japan Society for the Promotion of Science

Awards: ゼータ元の多角的研究, Research on the equivariant Tamagawa number conjecture and higher rank Iwasawa theory, 岩澤理論の同変化と精密化