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K-Theory and Intersection Theory

  • Henri Gillet

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 CD 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 k n , with dim(Y) + dim(Z) = n and for which YZ consists of a finite number of points.

Keywords

Spectral Sequence Chern Class Intersection Theory Coherent Sheave Cartier Divisor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Henri Gillet
    • 1
  1. 1.Department of Mathematics, Statistics, and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA

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