Hodge theoretic invariants of algebraic cycles 
-- Phillip Griffiths

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Assuming the generalized Hodge conjecture and conjecture of
Bloch-Beilinson, and working  modulo torsion, we shall give a complete set
of Hodge-theoretic invariants for rational equivalence of algebraic cycles.
The main new ingredient that arises in higher codimension is that the
"unambiguous part" of the Hodge structure of the field of definition of the
cycle enters.

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Both lectures are based on
joint work with Mark Green.