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Explore the first lecture in a series on the Anticyclotomic Main Conjecture delivered by Haruzo Hida from UCLA as part of the "Automorphic Forms and the Bloch–Kato Conjecture" program at the International Centre for Theoretical Sciences. Delve into advanced topics in number theory focusing on the connections between automorphic forms and the arithmetic nature of special values of L-functions. Learn about the fundamental concepts underlying the Anticyclotomic Main Conjecture, which represents a crucial component in understanding the relationship between L-values and associated algebraic structures such as Chow groups and Selmer groups. Gain insights into how this conjecture fits within the broader framework of the Bloch-Kato conjecture, which generalizes the famous Birch and Swinnerton-Dyer conjecture. Discover the essential role that automorphic forms play in studying L-values and their foundational importance to recent progress in the field. This lecture serves as an introduction to sophisticated mathematical concepts that bridge complex L-functions, algebraic varieties, motives, and automorphic representations over global fields, providing essential background for researchers and advanced students working in arithmetic geometry and number theory.
