Silting Objects, Simple-Minded Collections, t-Structures and Co-t-Structures for Finite-Dimensional Algebras

Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded $t$-structures with length heart and (4) bounded co-$t$-structures. These correspondences are shown to commute with mutations and partial orders. The results are valid for finite-dimensional algebras. A concrete example is given to illustrate how these correspondences help to compute the space of Bridgeland's stability conditions.

2010 Mathematics Subject Classification: 16E35, 16E45, 18E30

Keywords and Phrases: silting object, simple-minded collection, t-structure, co-t-structure, mutation.

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