Description of mixed motives

Doosung Park

Published 2017-08-03Version 1

Assuming the K\"unneth type standard conjecture, we propose the definition of mixed motives. We study their formal properties, and we associate mixed motives to schemes smooth and separated over a field. This serves as a universal cohomology theory. We also discuss $\ell$-adic realizations, and we discuss an unconditional construction of 2-motives and their properties.