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Paper IPM / M / 16934  


Abstract:  
Silting theorem gives a generalization of the classical tilting theorem of Brenner and Butler for a 2term silting complex. In this paper, we give a relative version of a silting theorem for any abelian category which is a finite Rvariety 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 Rvariety and \X ∈ \K^{\bb}(\CX) is a 2term \CXrelative 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 torsionfree classes.
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