Smashing localizations of rings of weak global dimension at most one

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• 作者：Silvana Bazzoni^a ; ^{bazzoni@math.unipd.it" class="auth_mail" title="E-mail the corresponding author} ; Jan &Scaron ; ťoví ; ček^b ; ^{stovicek@karlin.mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 13D09 ; 18E35 ; secondary ; 16E45
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：10 January 2017
• 年：2017
• 卷：305
• 期：Complete
• 页码：351-401
• 全文大小：851 K

文摘

We show for a ring R of 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 in R. If, moreover, R is 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 ring R, and it holds precisely for those Prüfer domains which are strongly discrete.