Among Grothendieck’s manifold contributions to algebraic geometry is his emphasis on the search for a universal cohomology theory for algebraic varieties and a conjectured description of it in terms of motives [Ma]. Various authors have recently set out to describe the properties of and conjecturally define a cohomology theory for algebraic varieties, which has been baptized “motivic cohomology” by Beilinson, MacPherson, and Schechtman ([BMS],[Be],[Bl],[T],[L1],[L2]). It is hoped that this theory, when and if it is fully developed, will in some sense be universal and thus provide at least a partial response to Grothendieck’s question.
Spectral Sequence Finite Type Torsion Class Distinguished Triangle Quotient Field
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Manin, Ju I., Correspondences, motifs and monoidal transformations, (AMS translation series), Mathematics of the USSR-Sbornik 6 (1968), 439–469. (original in Matematiceskiï Sbornik 77 (119) (1968) 475–507)CrossRefGoogle Scholar