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Explore the Bloch-Kato Conjecture as it applies to CM modular forms and Rankin-Selberg convolutions in this advanced mathematical lecture delivered by Francesc Castella at the International Centre for Theoretical Sciences. Delve into the intricate connections between automorphic forms and the arithmetic nature of special values of L-functions, examining how these fundamental concepts relate to algebraic structures such as Chow groups and Selmer groups. Investigate the theoretical framework that extends beyond the classical Birch and Swinnerton-Dyer conjecture to encompass the broader Bloch-Kato conjecture, which proposes far-reaching generalizations in understanding L-values associated with algebraic varieties, motives, and automorphic representations over global fields. Discover recent developments in this active area of number theory research, focusing specifically on complex multiplication (CM) modular forms and their associated Rankin-Selberg L-functions, while gaining insights into the sophisticated mathematical techniques used to study these deep arithmetic phenomena that lie at the intersection of algebraic number theory, automorphic forms, and algebraic geometry.
