论文标题
整数值多项式的本地化及其PICARD组的本地化
Localizations of integer-valued polynomials and of their Picard group
论文作者
论文摘要
我们证明了整数价值多项式的环，在本地化下表现得很好。然后，我们研究了$ \ mathrm {int}（d）$的PICARD组如何以及商组$ \ Mathcal {p}（d）：= \ m atrmrm {pic}（\ Mathrm {int}（int}（d）（d））/\ mathrm {pic}（pic}（pic} $特别是，我们表明$ \ MATHCAL {p}（d）\ simeq \ bigoplus \ mathcal \ mathcal {p}（t）$当$ t $ ranges在$ d $的jaffard家族中时，并且在$ d $ t $ t $ ranges时会在$ d $的jaffard家族中进行研究。特别是，我们表明，当$ d $是一个几乎是Dedekind域时，以前的同构是存在的，因此环形整数值的多项式在本地化下表现良好，因此$ d $的最大空间相对于逆拓扑而散布。
We prove a necessary and sufficient criterion for the ring of integer-valued polynomials to behave well under localization. Then, we study how the Picard group of $\mathrm{Int}(D)$ and the quotient group $\mathcal{P}(D):=\mathrm{Pic}(\mathrm{Int}(D))/\mathrm{Pic}(D)$ behave in relation to Jaffard, weak Jaffard and pre-Jaffard families; in particular, we show that $\mathcal{P}(D)\simeq\bigoplus\mathcal{P}(T)$ when $T$ ranges in a Jaffard family of $D$, and study when similar isomorphisms hold when $T$ ranges in a pre-Jaffard family. In particular, we show that the previous isomorphism holds when $D$ is an almost Dedekind domain such that the ring integer-valued polynomials behave well under localization and such that the maximal space of $D$ is scattered with respect to the inverse topology.
