Motive (algebraic geometry)

In algebraic geometry, a motive (or sometimes motif, following French usage) 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.

Source: Wikipedia — Motive (algebraic geometry) (CC BY-SA 4.0)