Reference Work Entry

Handbook of K-Theory

pp 351-428

Algebraic K-Theory, Algebraic Cycles and Arithmetic Geometry

  • Bruno KahnAffiliated withInstitut de Mathématiques de Jussieu Equipe Théories Géométriques, Université Paris 7


Warning: This chapter is full of conjectures. If you are allergic to them it may be harmful to your health. Parts of them are proven, though.

In algebraic geometry, one encounters two important kinds of objects: vector bundles and algebraic cycles. The first lead to algebraic K-theory while the second lead to motivic cohomology. They are related via the Chern character and Atiyah–Hirzebruch-like spectral sequences.