An intersection multiplicity in terms of 𝐸𝑥𝑡-modules

Chan, C-Y.

doi:10.1090/S0002-9939-01-06022-1

An intersection multiplicity in terms of $\textrm {Ext}$-modules
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Proc. Amer. Math. Soc. 130 (2002), 327-336 Request permission

Abstract:

The main aim of this paper is to discuss the relation between Serre’s intersection multiplicity and the Euler form. The Euler form is defined to be an alternating sum of the length of $\textrm {Ext}$-modules and is used by Mori and Smith to develop intersection theory over noncommutative rings. We show that they differ by a sign and that this relation is closely related to Serre’s vanishing theorem.

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