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arXiv · 2210.17337

Cancellation of projective modules in polynomial rings of prime characteristic

Sourjya Banerjee
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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 $P/ P$ 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.

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Sourjya Banerjee. 2022-10-31. Cancellation of projective modules in polynomial rings of prime characteristic. https://arxiv.org/abs/2210.17337

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