Kolyvagin Systems of Gauss Sum Type and the Structure of Selmer Groups

Explore advanced techniques in algebraic number theory through this conference lecture that examines Kolyvagin systems of Gauss sum type and their applications to understanding Selmer group structures. Delve into the sophisticated mathematical framework connecting automorphic forms to the arithmetic properties of L-functions, with particular focus on how Kolyvagin systems provide tools for analyzing the algebraic structures underlying the Bloch-Kato conjecture. Learn about the construction and properties of these specialized systems, their relationship to Gauss sums, and how they illuminate the structure of Selmer groups associated to Galois representations. Discover the connections between these theoretical constructs and central problems in arithmetic geometry, including generalizations of the Birch and Swinnerton-Dyer conjecture. Gain insights into recent developments in the field that bridge automorphic forms and arithmetic algebraic geometry, presented as part of a comprehensive program on automorphic forms and the Bloch-Kato conjecture at the International Centre for Theoretical Sciences.