Vitória, Jorge Perverse coherent t-structures through torsion theories. (English) Zbl 1314.14036 Algebr. Represent. Theory 17, No. 4, 1181-1206 (2014). Let \(K\) be an algebraically closed field, \(X\) a scheme of finite type over \(K\). Extending the work of Deligne, D. Arinkin and R. Bezrukavnikov [Mosc. Math. J. 10, No. 1, 3–29 (2010; Zbl 1205.18010)] defined an analogue perverse t-structure on \(\mathcal{D}^b(X)\), the derived category of coherent sheaves on \(X\) (they even defined it more a more general class of algebraic stacks). In this article, the author provides a new construction of the perverse t-structure mentioned above in the case of smooth, projective schemes \(X\) via graded modules, torsion theories and tilting. This method, which is based on D. Happel et al. [Mem. Am. Math. Soc. 575, 88 p. (1996; Zbl 0849.16011)], has new applications as it also allows to define similar perverse t-structures for the derived category of quasi-coherent sheaves over certain non-commutative projective planes as in the work of Artin and Schelter (see [M. Artin and W. F. Schelter, Adv. Math. 66, 171–216 (1987; Zbl 0633.16001)]). These applications are also explained in the article under review. Reviewer: Lennart Galinat (Köln) Cited in 3 Documents MSC: 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 13D09 Derived categories and commutative rings 13D30 Torsion theory for commutative rings 16E35 Derived categories and associative algebras 16S38 Rings arising from noncommutative algebraic geometry 16W50 Graded rings and modules (associative rings and algebras) Keywords:t-structure; torsion theory; perverse coherent sheaves; noncommutative projective planes Citations:Zbl 1205.18010; Zbl 0849.16011; Zbl 0633.16001 PDFBibTeX XMLCite \textit{J. Vitória}, Algebr. Represent. 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