An intersection multiplicity in terms of Ext-modules

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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 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.

Original languageEnglish
Pages (from-to)327-336
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - 2002


  • Chern character
  • Euler characteristic
  • Euler form
  • Intersection multiplicity


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