On a question of nori: the local case

Euler class groups and a theorem of Roitman

“…Let m be a maximal ideal of A. It is an obvious consequence of the main result of Mandal-Varma [11], that E n (A m [T ]) = 0. Now it follows from Theorem 3.9 that Φ : E n (A) ↩→ E n (A[T ]) is surjective and hence an isomorphism.…”

“…The method of proof is the same as the above theorem. We only need to note that for a maximal ideal m of A, by a result of Mandal-Varma [11] one has IA m = (h 1 , . .…”

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

“…The following corollary is an improvement of [MV,Theorem 4]. The proof is the same as that of (4.8).…”

Local coefficients and Euler class groups

“…Essentially, all the conjectures given at the time when the program was outlined were proved and the program of Nori flourished beyond all expectations. Among the major and important papers on this program are [M,MS,MV,BRS1,BRS2,BRS3,BhDaMa]. Readers are referred to [MaSh] for further introductory remarks and history [MkM,Mk,Mu1] of development of obstruction theory in algebra.…”