Mixed realizations, mixed motives and Hodge and Tate conjectures for singular varieties

Abstract

This chapter is a continuation of the previous one. Jannsen’s formalism of mixed realizations and mixed motives is discussed. These are defined as extensions of their pure analogues and the corresponding categories should be tannakian. Deligne has suggested a somewhat different definition of mixed motives, but in both Jannsen’s and his conception the fundamental notion has become the realization.