Luca Barbieri Viale: Theoretical motives revisited and developed

Abstract: The approach to mixed motives through universal cohomology theories is revisited and developed. These universal theories are obtained via representing 2-functors yielding universal abelian categories of T-motives. Eilenberg-Steenrod axioms are included: there are ordinary homologies with values in abelian categories for any homological structure on a category and the ordinary theories are representable. The universal ordinary theory on CW-complexes yields hieratic R- modules and considering the theory generated by singular homology we get back R-modules. For geometric categories like schemes or manifolds, adding vanishing and duality axioms, shall be sufficient to get mixed motives as T-motives.