Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined intersection products. Samuel formalized the concept of an adequate equivalence relation in 1958 . Since then it has become central to theory of motives. For every adequate equivalence relation, one may define the category of pure motives with respect to that relation.

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