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motive

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motive

conjectural objects in algebraic geometry that provide a universal cohomology theory of varieties

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About motive

In algebraic geometry, a motive is an abstract object introduced by Alexander Grothendieck in the 1960s as part of a proposed universal cohomology theory for algebraic varieties. The idea is that theories such as Betti cohomology, de Rham cohomology, etale cohomology, and crystalline cohomology should arise as different realizations of the same underlying object. Thus, a motive of a variety is meant to capture the part of its geometry common to these cohomology theories.

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