Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras

By S. Koenig, Dong Ping Yang. Documenta Mathematica, 2012

220 citations recorded by the source corpus.

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. The results are valid for finite- dimensional non-positive differential graded algebras, in particular for finite dimensional alge- bras. A concrete example is given to illustrate how these correspondences help to compute the space of Bridgeland's stability conditions. MSC 2010 classification: 16E35, 16E45, 18E30.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5340752a1f681739b93f5b091354c9f04e33d94c

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Citations in the corpus

Semibricks (2016, background): “A simple-minded collection in Db(modA) always consists of nA objects, and if it is 2-term, each of the objects belongs to either modA or (modA)[1], see [21, 8].”
Discreteness of silting objects and t ‐structures in triangulated categories (2017, methodology): “In the situations of [48, 50, 67] and the forthcoming paper by Keller–Nicolás, there are natural ST-pairs and for these ST-pairs our map coincides with the maps in these papers.”