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Explore the fourth lecture in Kentaro Nakamura's series on the Local Epsilon Conjecture, presented as part of the "Automorphic Forms and the Bloch–Kato Conjecture" program at the International Centre for Theoretical Sciences. This 1 hour 33 minute lecture contributes to a program focused on recent developments connecting automorphic forms with the arithmetic of special values of L-functions. The program addresses a central problem in number theory: understanding the arithmetic nature of special values of complex L-functions associated with algebraic varieties, motives, or automorphic representations over global fields, and connecting these L-values to orders of algebraic structures like Chow groups or Selmer groups. The Birch and Swinnerton-Dyer conjecture serves as a key example, while the Bloch-Kato conjecture offers a broader generalization. Designed for students and researchers interested in number theory, this lecture is part of ICTS's commitment to building an inclusive, non-discriminatory environment welcoming diverse participants.
