Notes on absolute Hodge classes
نویسندگان
چکیده
Absolute Hodge classes first appear in Deligne’s proof of the Weil conjectures for K3 surfaces in [14] and are explicitly introduced in [16]. The notion of absolute Hodge classes in the singular cohomology of a smooth projective variety stands between that of Hodge classes and classes of algebraic cycles. While it is not known whether absolute Hodge classes are algebraic, their definition is both of an analytic and arithmetic nature. The paper [14] contains one of the first appearances of the notion of motives, and is among the first unconditional applications of motivic ideas. Part of the importance of the notion of absolute Hodge classes is indeed to provide an unconditional setting for the application of motivic ideas. The papers [14], [17] and [1], among others, give examples of this train of thought. The book [23] develops a theory of mixed motives based on absolute Hodge classes.
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