Riemann-Roch Algebra pp 151-196 | Cite as

# An Intersection Formula. Variations and Generalizations

## 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.

## Keywords

Exact Sequence Intersection Formula Coherent Sheave Coherent Sheaf Grothendieck Group## Preview

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