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K-Theory and Intersection Theory

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Handbook of K-Theory

Abstract

The problem of defining intersection products on the Chow groups of schemes has a long history. Perhaps the first example of a theorem in intersection theory is Bézout’s theorem, which tells us that two projective plane curves C and D, of degrees c and d and which have no components in common, meet in at most cd points. Furthermore if one counts the points of C ∩ D with multiplicity, there are exactly cd points. Bezout’s theorem can be extended to closed subvarieties Y and Z of projective space over a field k, ℙ n k , with dim(Y) + dim(Z) = n and for which Y ∩ Z consists of a finite number of points.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 60607-7045, Chicago, IL, USA

    Henri Gillet

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  1. Henri Gillet
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Editors and Affiliations

  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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Gillet, H. (2005). K-Theory and Intersection Theory. In: Friedlander, E., Grayson, D. (eds) Handbook of K-Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27855-9_7

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