Lorentz Center - Annual EAGER Conference 2004 Workshop Algebraic Cycles and Motives from 30 Aug 2004 through 3 Sep 2004
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    Annual EAGER Conference 2004
    Workshop Algebraic Cycles and Motives
    from 30 Aug 2004 through 3 Sep 2004

 
The theory of algebraic cycles deals with the study of subvarieties of a given algebraic variety

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.



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