Abstract
The first point of this chapter is to develop a commutative diagram similar to that of the Riemann-Roch theorems, and called the Intersection Formula for the K-functor. In particular, this will show how the product in the ring K(X) relates to the geometric intersection of subschemes of X. From this intersection formula for K we deduce a corresponding formula for Gr K, which is analogous to the “excess intersection formula” of [FM], cf. [F 2], Theorem 6.3. Special cases of the intersection formula are contained in [SGA 6] and [Man], but the general version given here for K-theory seems to be new. Our proof eliminates the use of Tor, and gives another striking illustration of the deformation formalism of Chapter II.
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© 1985 Springer Science+Business Media New York
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Fulton, W., Lang, S. (1985). An Intersection Formula. Variations and Generalizations. In: Riemann-Roch Algebra. Grundlehren der mathematischen Wissenschaften, vol 277. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1858-4_6
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DOI: https://doi.org/10.1007/978-1-4757-1858-4_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3073-6
Online ISBN: 978-1-4757-1858-4
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