Algebraic K-Theory, Algebraic Cycles and Arithmetic Geometry

Bruno Kahn ()
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Bruno Kahn: Université Paris 7, Institut de Mathématiques de Jussieu Equipe Théories Géométriques

Chapter II.4 in Handbook of K-Theory, 2005, pp 351-428 from Springer

Abstract: Abstract 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.

Keywords: Zeta Function; Spectral Sequence; Abelian Variety; Smooth Projective Variety; Algebraic Cycle (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/978-3-540-27855-9_9

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