On the tangent space to the space of algebraic cycles
-- Phillip Griffiths

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Motivated by classical results of Mumford and Bloch, we shall
propose a definition of the tangent space to the space of 0-cycles on a
smooth algebraic variety (the definition for general codimensional cycles
requires one further technical step). Although it is algebraic, the
definition is motivated by geometric considerations and reveals on the level
of cycles phenomena known for Chow groups. One geometric consequense is a
geometric existence theorem giving a proof of the Bloch-Beilinson conjecture
for 0-cycles on surfaces "to first order".




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Both lectures are based on
joint work with Mark Green.