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Annual EAGER Conference 2004 |
The theory of
algebraic cycles deals with the study of subvarieties of a given algebraic
variety. An algebraic cycle is defined as a formal linear combination of
irreducible subvarieties of a given codimension. The set of cycles is unwieldy:
one has to put suitable equivalence relations on this set and these in general
only work well for non-singular projective varieties. Indeed, for such
varieties there is a good equivalence relation, rational equivalence, such that
the set of classes of algebraic cycles endowed with the intersection product
becomes a ring, the Chow ring; the goal of the theory is to understand the
structure of this ring. To this end, the main tool is to study the relationship
of the Chow ring with the cohomology ring for various cohomology theories. Over
the complex numbers we may use any of the usual cohomology theories from
algebraic topology (a “classical” cohomology theory). This comparison leads to
the famous Hodge conjecture (predicting that an algebraic cycle can be
characterized in classical cohomology as having pure type under the Hodge
decomposition) and to Grothendieck's theory of motives (which, roughly speaking,
can be thought of as the “universal cohomology theory” for algebraic
varieties). The aim of the
workshop is to bring together a number of the leading researchers in this field
on the occasion of the 75th birthday of Prof. J.P. Murre. The theory of
algebraic cycles and motives has always been at the center of Prof. Murre's
research. He has made important contributions to the subject and has initiated
the study of algebraic cycles in the Netherlands. He also collaborated with a
large number of people in the subject, several of whom we are inviting. The
invited speakers are requested to either give a talk on their current research
or to give an overview lecture suitable for a larger audience. They are all
expected to take part in discussions with the younger researchers. [Back] |