Special Cycles on Moduli Spaces of Unitary Shtukas and Higher Derivatives - Lecture 3

Explore advanced topics in algebraic geometry and number theory through this lecture examining special cycles on moduli spaces of unitary shtukas and their higher derivatives. Delve into the intricate connections between automorphic forms and the arithmetic properties of L-functions as part of a comprehensive program on the Bloch-Kato conjecture. Learn about the geometric structures underlying moduli spaces of unitary shtukas, which serve as crucial objects in the Langlands program and arithmetic geometry. Investigate how special cycles arise naturally in these moduli spaces and their relationship to higher derivative constructions. Understand the role these mathematical objects play in connecting L-values to algebraic structures such as Chow groups and Selmer groups, contributing to our understanding of fundamental conjectures in number theory including the Birch and Swinnerton-Dyer conjecture and its generalizations. Gain insights into cutting-edge research methodologies that bridge automorphic forms with arithmetic geometry, essential for advancing our comprehension of special values of complex L-functions associated with algebraic varieties and motives over global fields.