27 - Motivating Motives previous

Pure motives are just a special case of "mixed motives",
which aim to handle varieties that are not smooth, or not projective.

These are also mysterious —
but Voevodsky essentially managed to define the derived category of mixed motives
without defining mixed motives themselves!
In 1996 he used these ideas to solve the Milnor conjecture, triggering a burst of new work.


So, motives continue to tantalize and inspire!