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Explore the intricate world of eigenvarieties and their significance in arithmetic through this 57-minute lecture by Daniel Barrera Salazar from Universidad de Santiago de Chile. Delve into the concept of eigenvarieties as moduli spaces of p-adic automorphic forms for reductive groups, with a focus on classical points representing algebraic automorphic forms. Examine the crucial connection between the local geometry of eigenvarieties surrounding classical points and the special values of L-functions, gaining insights into this important area of mathematical research.
