K-Theory and Intersection Theory

Henri Gillet ()
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Henri Gillet: University of Illinois at Chicago, Department of Mathematics, Statistics, and Computer Science

Chapter II.2 in Handbook of K-Theory, 2005, pp 235-293 from Springer

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

Keywords: Spectral Sequence; Chern Class; Intersection Theory; Coherent Sheave; Cartier Divisor (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/978-3-540-27855-9_7

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