Claudio PEDRINI
(Università degli Studi di Genova)
Finite dimensional motives and the conjectures of Bloch and
Beilinson
We will relate the notion of finite dimensionality in the triangulated category DM(k) of
motivic complexes over a field k ,constructed by Voevodsky, with the Conjectures by Beilinson
and
Bloch on the existence of a finite filtration on the Chow groups of smooth projective varieties.
According to a recent result announced by J.Ayoub all objects in DM(k) are Schur-finite
dimensional.
This result in particular implies the proof of a long-standing Conjecture in Algebraic Geometry:
Bloch's Conjecture about the vanishing of the Albanese Kernel for complezx surfaces of general
type
with geometric genus =0.