Torsion pairs via large silting mutation
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In abstract algebra, an “algebra” has a highly rich structure which can be approximated by “modules”; in particular, it can be studied via its category of modules. A “torsion pair” gives a unique decomposition of this category into semi-orthogonal subcategories, simplifying its study. It is known that certain torsion pairs are in bijection with “2-term silting complexes”, for which any essential block can be replaced by a different one such that the resulting complex is of the same type. This operation, called “silting mutation”, induces mutations on the corresponding torsion pairs. Moreover, arbitrary torsion pairs are in bijection with “2-term cosilting complexes”, the infinite-dimensional dual of the former. The latter have a conceptually distinct operation of “cosilting mutation”, which does not guarantee that the cosilting mutation of a 2-term cosilting complex is once again 2-term, and thus that it corresponds to a torsion pair. In this talk, we introduce an infinite-dimensional analog of silting mutation and show it can be applied to 2-term cosilting complexes, providing a reinterpretation of cosilting mutation while also inducing mutations on arbitrary torsion pairs. Links: slides.