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On triviality of the Euler class group of a deleted neighbourhood of a smooth local scheme

Author: Mrinal Kanti Das
Journal: Trans. Amer. Math. Soc. 365 (2013), 3397-3411
MSC (2010): Primary 13C10, 19A15, 13H05, 13B40
Published electronically: December 12, 2012
MathSciNet review: 3042589
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Abstract: Let $ (R, \mathfrak{m})$ be a regular local ring of dimension $ d$ which is essentially of finite type over a field $ k$ such that the residue field of $ R$ is infinite. Let $ f \in \mathfrak{m} \smallsetminus \mathfrak{m}^2$ be a regular parameter and $ n$ be an integer such that $ 2n \geq d + 1$. Let $ I \subset R_f$ be an ideal of height $ n$ such that $ I/I^2$ is generated by $ n$ elements. It is proved that any given set of $ n$ generators of $ I/I^2$ can be lifted to a set of $ n$ generators of $ I$.

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Additional Information

Mrinal Kanti Das
Affiliation: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108 India

Received by editor(s): October 15, 2010
Received by editor(s) in revised form: March 25, 2011
Published electronically: December 12, 2012
Dedicated: Dedicated to Professor S. M. Bhatwadekar on his 65th birthday
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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