Cancellation of projective modules in polynomial rings of prime characteristic

Sourjya Banerjee

Cancellation of projective modules in polynomial rings of prime characteristic

Commutative Algebra 2022-12-15 v3

Authors: Sourjya Banerjee

Abstract

Let $A$ be a commutative Noetherian ring of characteristic $p>0$ , such that $\dim(A)=d$ . Let $P$ be a projective $A[T_1,...,T_n]$ -module of rank $d$ . We show that $P$ is cancellative if and only if $P/<T_1,...,T_n>P$ is cancellative. We deduce some applications. In one of the interesting consequences, we show that the Bass-Quillen conjecture has an affirmative answer in dimension three, when $2$ is invertible.

Keywords

projective modules polynomial rings prime characteristic cancellation Bass-Quillen conjecture Noetherian ring

Cite

@article{arxiv.2210.17337,
  title  = {Cancellation of projective modules in polynomial rings of prime characteristic},
  author = {Sourjya Banerjee},
  journal= {arXiv preprint arXiv:2210.17337},
  year   = {2022}
}

Comments

The proof of 2.2 is not correct

Cancellation of projective modules in polynomial rings of prime characteristic

Abstract

Keywords

Cite

Comments

Related papers