On t-Structures and Tilting Theory

Abstract

Let A be a right coherent associative ring with unit. We introduce the notion of coendofinite complex and we associate to such a complex a t-structure in D ^b (mod A). We give conditions for the heart of that t-structure to be a module category. We also give some applications in connection with derived equivalent rings and tilting theory. In particular for a tilting module over a finite dimensional k-algebra, we get a reformulation of Brenner-Butler's theorem in terms of t-structures.

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Acknowledgments

We would like to thank Leovigildo Alonso, Ana Jeremias, Henning Krause and Manuel Saorin for helpful comments and ideas.

This work was completed during several trips between Spain, Argentina and Canada. The first author was partially supported by Xunta de Galicia through the research project XUGA20701A96 and the second author was partially supported by Conicet, Argentina. Both authors thanks professor Ibrahim Assem for his kind invitation to the University of Sherbrooke, Quebec, Canada.