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This lecture is the third installment in Kentaro Nakamura's series on the Local Epsilon Conjecture, presented at the International Centre for Theoretical Sciences as part of the "Automorphic Forms and the Bloch–Kato Conjecture" program. Delve into advanced number theory concepts connecting automorphic forms with the arithmetic of special values of L-functions. The program explores 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 researchers and students interested in the Birch and Swinnerton-Dyer conjecture and its generalizations through the Bloch-Kato conjecture. The complete program runs from May 19-30, 2025, at the Ramanujan Lecture Hall in ICTS Bengaluru, welcoming diverse participants interested in these mathematical frontiers.
