 Alexander Grothendieck's standard conjectures on algebraic cycles yield enough cycles to construct his category of motives and would imply that algebraic cycles play a vital role in any cohomology theory of algebraic varieties.Conversely, Alexander Beilinson proved that the existence of a category of motives implies the standard conjectures.Additionally, cycles are connected to algebraic "K"-theory by Bloch's formula, which expresses groups of cycles modulo rational equivalence as the cohomology of "K"-theory sheaves.