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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An intersection multiplicity in terms of $\textrm{Ext}$-modules


Author: C-Y. Jean Chan
Journal: Proc. Amer. Math. Soc. 130 (2002), 327-336
MSC (2000): Primary 13D22, 13H15, 14C17, 13D07
Published electronically: May 25, 2001
MathSciNet review: 1862109
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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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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

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06022-1
PII: S 0002-9939(01)06022-1
Keywords: Intersection multiplicity, Chern character, Euler characteristic, Euler form
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
Article copyright: © Copyright 2001 American Mathematical Society