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This lecture, part of the "Automorphic Forms and the Bloch–Kato Conjecture" program at the International Centre for Theoretical Sciences, features Kentaro Nakamura presenting the first installment of his series on the Local Epsilon Conjecture. Explore fundamental concepts in number theory connecting automorphic forms with the arithmetic of special values of L-functions. The program focuses on recent developments in understanding the arithmetic nature of special values of complex L-functions associated with algebraic varieties, motives, or automorphic representations over global fields, and their connections to orders of algebraic structures like Chow groups or Selmer groups. Particularly relevant for students and researchers interested in the Birch and Swinnerton-Dyer conjecture and its generalizations through the Bloch-Kato conjecture. The complete lecture runs for 1 hour and 43 minutes and is part of a broader program organized by Ashay Burungale, Haruzo Hida, Somnath Jha, and Ye Tian.
