Algebraic Cycles and Algebraic Aspects of Cohomology and K-Theory

Abstract

These are the notes of the lectures delivered at the C.I.M.E. meeting in Torino, June 93. I have tried to keep the written version as much as possible in the informal style of the lectures. The content of the eight lectures is grouped into seven chapters. In my lectures, with the exception of chapters 4 and 5, the emphasis was on the algebraic methods in studying algebraic cycles; as such the lectures complement those of C. Voisin and M. Green. The chapters are as follows:

• 1. Algebraic cycles. Basic notions.

• 2. The Chow ring and the Grothendieck group of coherent sheaves.

• 3. The Chow ring and higher algebraic K-theory.

• 4. Introduction to the Deligne-Beilinson cohomology.

• 5. The Hodge-Conjecture.

• 6. Applications of the theorem of Merkurjev and Suslin to the theory of algebraic cycles of codimension two.

• 7. Grothendieck’s theory of motives.