Special Cycles on Moduli Spaces of Unitary Shtukas and Higher Derivatives - Lecture 2

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 shtukas, which serve as function field analogues of Shimura varieties, and understand how special cycles contribute to our understanding of arithmetic intersection theory. Examine the role of these mathematical objects in connecting L-values to algebraic structures such as Chow groups and Selmer groups, building upon foundational concepts in the Birch and Swinnerton-Dyer conjecture. Discover how unitary shtukas provide a framework for studying automorphic representations over global function fields and their associated L-functions. Gain insights into recent developments in arithmetic geometry that bridge classical number theory with modern algebraic techniques, particularly focusing on how special cycles encode arithmetic information about L-functions and their derivatives.