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On a question of Moshe Roitman and Euler class of stably free module
Journal
Journal of Algebra
ISSN
00218693
Date Issued
2023-01-15
Author(s)
Keshari, Manoj K.
Tikader, Soumi
Abstract
Let A be a ring of dimension d containing an infinite field k, T1,…,Tr be variables over A and P be a projective A[T1,…,Tr]-module of rank n. Assume one of the following conditions holds. (1) 2n≥d+3 and P is extended from A. (2) 2n≥d+2, A is an affine F‾p-algebra and P is extended from A. (3) 2n≥d+3 and singular locus of Spec(A) is a closed set V(J) with ht J≥d−n+2. Assume Um(Pf)≠∅ for some monic polynomial f(Tr)∈A[T1,…,Tr]. Then Um(P)≠∅ (see 6.1).
Volume
614
Publication link
Subjects