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Perverse Coherent t-Structures Through Torsion Theories

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Abstract

Bezrukavnikov, later together with Arinkin, recovered Deligne’s work defining perverse t-structures in the derived category of coherent sheaves on a projective scheme. We prove that these t-structures can be obtained through tilting with respect to torsion theories, as in the work of Happel, Reiten and Smalø. This approach allows us to define, in the quasi-coherent setting, similar perverse t-structures for certain noncommutative projective planes.

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  1. Fakultät für Mathematik, Universität Bielefeld, 33501, Bielefeld, Germany

    Jorge Vitória

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  1. Jorge Vitória
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Correspondence to Jorge Vitória.

Additional information

Most of this work was developed at the University of Warwick and supported by FCT (Portugal), research grant SFRH/BD/28268/2006. Later, this project was also supported by DFG (SPP 1388) in Stuttgart and by SFB 701 in Bielefeld. The author would like to thank Steffen Koenig, Qunhua Liu, Dmitriy Rumynin, Jan Š\(\check{t}\)ovíček and the anonymous referee for valuable comments on the previous versions of this paper.

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Vitória, J. Perverse Coherent t-Structures Through Torsion Theories. Algebr Represent Theor 17, 1181–1206 (2014). https://doi.org/10.1007/s10468-013-9441-z

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