标题： 相干$I$-索引代数和非交换射影概形 显示英文标题

标题： Coherent $I$-indexed algebras and noncommutative projective schemes

摘要： 我们研究以$I$为索引集的相干代数及其相关的非交换射影概形，其中索引集$I$是一个局部有限的定向偏序集。 我们的主要结果是通过具有类似于充足线丛的张量幂序列性质的对象序列来表征此类非交换射影概形，这扩展了Polishchuk针对相干$\mathbb{Z}$为索引集的代数给出的类似表征。 显示英文摘要

摘要： We study coherent $I$-indexed algebras and associated noncommutative projective schemes, where the index set $I$ is a locally finite directed poset. Our main result is a characterisation of such noncommutative projective schemes in terms of sequences of objects with properties analogous to the sequence of tensor powers of an ample line bundle, extending a similar characterisation given by Polishchuk for coherent $\mathbb{Z}$-indexed algebras.