On the transcendental part of the motive of a surface
-- Claudio Pedrini

<p>

This is joint  work with B. Kahn and
J. Murre. We introduce a new birational invariant, the transcendental part 
t_2(S) of the  Chow motive h_2(S) of an algebraic surface S.   We compute its
endomorphism group and relate it to the conjectures of Bloch and Beilinson.