Smashing localizations of rings of weak global dimension at most one
Smashing localizations of rings of weak global dimension at most one
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粉碎弱全局维度环的局部化至多一个
DOI：
10.1016/j.aim.2016.09.028
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发表时间：
2014
影响因子：
1.7
通讯作者：
J. Šťovíček
中科院分区：
文献类型：
--
作者：
S. Bazzoni;J. Šťovíček
证明了对于一个至多一个弱整体维环，它的派生范畴的粉碎子范畴与从INR开始的同调满同态的等价类之间存在一个双射。此外，如果R是可交换的，我们证明了紧生成的局部化的子范畴精确地对应于平坦的满同态。我们还对任意赋值整环的派生范畴的Smash局部化进行了分类，并给出了对任意弱整体维交换环的望远镜猜想(TC)的一个简单判据。因此，我们证明了TC对于任何交换的von Neumann正则环R都成立，并且对于那些强离散的Prüfer域精确地成立。
We show for a ringRof weak global dimension at most one that there is a bijection between the smashing subcategories of its derived category and the equivalence classes of homological epimorphisms starting inR. If, moreover,Ris commutative, we prove that the compactly generated localizing subcategories correspond precisely to flat epimorphisms. We also classify smashing localizations of the derived category of any valuation domain, and provide an easy criterion for the Telescope Conjecture (TC) for any commutative ring of weak global dimension at most one. As a consequence, we show that the TC holds for any commutative von Neumann regular ringR, and it holds precisely for those Prüfer domains which are strongly discrete.
影响因子：
1.1
作者：
D. Benson;S. Iyengar;H. Krause
通讯作者：
D. Benson;S. Iyengar;H. Krause
影响因子：
1.9
作者：
D. Benson;S. Iyengar;H. Krause
通讯作者：
D. Benson;S. Iyengar;H. Krause