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

E-ISSN： 1865-5394|8|3|451-480

ISSN： 1865-2433

Source： Journal of K-Theory, Vol.8, Iss.3, 2011-12, pp. : 451-480

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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 If the smoothness assumption is removed, the result of Bhatwadekar-Sridharan is no longer valid and also the Euler class groups above are not in general isomorphic.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.