对“非交换空间之间的映射”一文的勘误 [Trans. Amer. Math. Soc., 356(7) (2004) 2927-2944]
环与代数
2016-01-28 v2
摘要
已发表论文中引理3.1的陈述不正确。引理3.1是定理3.2证明所必需的。定理3.2如最初陈述的那样是正确的，但其“证明”不正确。在此我们修改引理3.1和定理3.2的陈述与证明。我们还证明了一个新结果。设k为一个域，A为一个左、右诺特的N-分次k-代数，且对所有n满足dim_k(A_n)<∞，J为A的一个分次双边理想。若非交换概型Proj_{nc}(A)同构于一个射影概型X，则存在一个闭子概型Z ⊆ X，使得Proj_{nc}(A/J)同构于Z。此结果是我们实际证明内容的几何翻译：若范畴QGr(A)等价于Qcoh(X)，则QGr(A/J)等价于Qcoh(Z)，其中Z ⊆ X为某个闭子概型。
引用
@article{arxiv.1507.02497,
title = {Corrigendum to "Maps between non-commutative spaces" [Trans. Amer. Math. Soc., 356(7) (2004) 2927-2944]},
author = {S. Paul Smith},
journal= {arXiv preprint arXiv:1507.02497},
year = {2016}
}
备注
v2 changed after referee's report. Added a hypothesis on A in Lemma 1.1 to ensure that the first left derived functor exists. In Lemma 1.1(2) an isomorphism is replaced by an equality and the proof is changed accordingly. Small change to the statement of Theorem 1.3