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Explore local Tate duality in the context of positive characteristic fields through this advanced mathematical lecture delivered at the International Centre for Theoretical Sciences. Delve into the fundamental principles and applications of local Tate duality, a crucial tool in algebraic number theory and arithmetic geometry, specifically examining its behavior and properties when working over fields of positive characteristic. Learn how this duality theory connects to broader themes in the study of automorphic forms and the Bloch-Kato conjecture, providing essential background for understanding the arithmetic nature of special values of L-functions. Gain insights into the technical aspects of local field theory and how duality theorems serve as foundational tools for investigating algebraic structures such as Chow groups and Selmer groups in positive characteristic settings.
