The aim of this paper is to formulate the Iwasawa main conjecture for varieties (or motives) over arbitrary number fields. See (4.9) for the statement of the conjecture, and (4.15) for "philosophical comments" on it. To formulate our conjecture, we need the p-aic Hodge theory developed by Tate [T 2 ], Fontaine and Messing [FM], and Faltings [FJ.
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Kazuya Katô (1993) studied this question.