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Revisiting Nori's question and homotopy invariance of Euler class groups

Published online by Cambridge University Press:  05 November 2010

Mrinal Kanti Das
Mrinal Kanti Das
Affiliation:
Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108India. mrinal@isical.ac.in
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Abstract

This paper examines the relation between the Euler class group of a Noetherian ring and the Euler class group of its polynomial extension. When the ring is a smooth affine domain, the two groups are canonically isomorphic. This is a consequence of a theorem of Bhatwadekar-Sridharan, which they proved in order to answer a question of Nori on sections of projective modules over such rings. If the smoothness assumption is removed, the result of Bhatwadekar-Sridharan is no longer valid and also the Euler class groups above are not in general isomorphic. In this paper we investigate a variant of Nori's question for arbitrary Noetherian rings and derive several consequences to understand the relation between various groups in the theory of Euler classes.

Keywords

Projective modulesEfficient generation of idealsEuler class groups
Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 3 , December 2011 , pp. 451 - 480
Copyright
Copyright © ISOPP 2010

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