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Algebraic K-Theory, Algebraic Cycles and Arithmetic Geometry

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Handbook of K-Theory

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.

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  1. Institut de Mathématiques de Jussieu Equipe Théories Géométriques, Université Paris 7, Case 7012, 75251, Paris Cedex 05, France

    Bruno Kahn

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  1. Department of Mathematics, Northwestern University, 60208, Evanston, IL, USA

    Eric M. Friedlander

  2. Department of Mathematics, University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA

    Daniel R. Grayson

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Kahn, B. (2005). Algebraic K-Theory, Algebraic Cycles and Arithmetic Geometry. In: Friedlander, E., Grayson, D. (eds) Handbook of K-Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27855-9_9

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