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|Paper IPM / M / 16934||
Silting theorem gives a generalization of the classical tilting theorem of Brenner and Butler for a 2-term silting complex. In this paper, we give a relative version of a silting theorem for any abelian category which is a finite R-variety over some commutative Artinian ring R. To this end, the notion of relative silting complexes is introduced and it is shown that they play a similar role as silting complexes. It is shown that if \CX is a subcategory of \CA which is a dualizing R-variety and \X ∈ \K\bb(\CX) is a 2-term \CX-relative silting complex, then there are two torsion pairs, in \CA and in \mmod \End(\X)op together with a pair of crosswise equivalences between torsion and torsion-free classes.
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