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Explore deformations of reducible Galois representations with large Selmer p-rank in this 70-minute conference talk by Eknath Ghate from the International Centre for Theoretical Sciences. Delve into advanced topics in algebraic number theory as part of the "Automorphic Forms and the Bloch–Kato Conjecture" program, which examines recent developments and connections between automorphic forms and the arithmetic of special values of L-functions. Learn about the intricate relationships between Galois representations, Selmer groups, and their p-ranks, building upon foundational concepts in the study of L-functions and their special values. Gain insights into how these mathematical structures connect to broader conjectures in number theory, including the Birch and Swinnerton-Dyer conjecture and the far-reaching Bloch-Kato conjecture. Discover how automorphic forms serve as essential tools for studying L-values and understanding the arithmetic nature of special values of complex L-functions associated with algebraic varieties, motives, and automorphic representations over global fields.
