An intersection multiplicity in terms of $\textrm {Ext}$-modules
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Abstract:
The main aim of this paper is to discuss the relation between Serreâs 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 Serreâs vanishing theorem.References
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Additional Information
- C-Y. Jean Chan
- Affiliation: Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112
- Address at time of publication: Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, Indiana 47907-1395
- Email: cyjan@math.utah.edu
- Received by editor(s): October 11, 1999
- Received by editor(s) in revised form: June 15, 2000
- Published electronically: May 25, 2001
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 327-336
- MSC (2000): Primary 13D22, 13H15, 14C17, 13D07
- DOI: https://doi.org/10.1090/S0002-9939-01-06022-1
- MathSciNet review: 1862109