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Strong Euler class of a stably free module of odd rank

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Title Strong Euler class of a stably free module of odd rank
 
Creator DAS, MK
ZINNA, MA
 
Subject PROJECTIVE GENERATION
UNIMODULAR ROWS
EXTENSIONS
QUESTION
NORI
Projective modules
Euler class groups
Unimodular rows
 
Description Let R be a commutative Noetherian ring of dimension n >= 3. Following a suggestion of Fasel, we establish a group homomorphism phi from van der Kallen's group Um(n+1)(R)/En+1(R) to the n-th Euler class group E-n(R) so that: (1) when n is even, phi coincides with the homomorphism given by Bhatwadekar and Sridharan through Euler classes; (2) when n is odd, phi is non-trivial in general for an important class of rings; (3) the sequence Um(n+1)(R)/En+1(R) ->(phi) E-n(R) E-0(n)(R) -> 0 is exact, where E-0(n)(R) is the n-th weak Euler class group. (If X = Spec(R) is a smooth affine variety of dimension n over R so that-the complex-points of X are complete intersections and the canonical module K-R is trivial, then the sequence is proved to be exact on the left as well.) More generally, let R be a commutative Noetherian ring of dimension d and n be an integer such that n
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2016-01-14T14:11:09Z
2016-01-14T14:11:09Z
2015
 
Type Article
 
Identifier JOURNAL OF ALGEBRA, 432,185-204
0021-8693
1090-266X
http://dx.doi.org/10.1016/j.jalgebra.2015.03.007
http://dspace.library.iitb.ac.in/jspui/handle/100/17694
 
Language en