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A certain map-the "residue map"-is defined and its properties are investigated. The impetus for the definition and study of this map is a definition by A. Grothendieck of a homomorphism, the " residue symbol", which has been found applicable in several areas, including the duality theory of algebraic varieties.doi:10.2307/1999037 fatcat:4ezfes5eqfh27o4kf57rev6n4y