We consider functions on a projective system which satisfy a compatibility relation. At each step, the sum of the values in a given fiber are equal to the values at the base point. Mazur isolated this notion [Maz 1], [Maz 2], [Ma-SwD], which turns out to be very prevalent in number theory. This followed the work of Iwasawa, working with group rings formed with a projective system of finite groups, so that the compatibility relation is merely a formulation independent of the group for the basic property of the natural homomorphism of group rings induced by a group homomorphism. Iwasawa’s work dealt with projective limits of ideal class groups, a topic pursued especially in papers of Coates with Sinnott, Lichtenbaum and Wiles, [CS 1], [CS 2], [C-Li], [CW]. For projective limits of divisor class groups in the modular function field, cf. the Kubert-Lang series [KL].
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