From 2-term to d-term silting complexes

For a finite-dimensional algebra, it is known from the work of Adachi-Iyama-Reiten that two-term silting complexes are in bijection with functorially finite torsion pairs and support tau-tilting pairs in the module category. Later, more classes were added to these bijections, including complete cotorsion pairs, left-finite semibricks, and left-finite wide subcategories. In this talk, we will generalise the above bijections to arbitrary d-term silting complexes by introducing ’extended module categories’ or ’truncated derived categories’. We then provide appropriate generalisations of torsion classes, semibricks, and wide subcategories to extriangulated categories to show that d-term silting complexes are in bijection with functorially finite positive torsion pairs and complete hereditary cotorsion pairs. We will also show them to be in bijection with left-finite semibricks and left-finite wide subcategories in the extended module category. This talk is based on a joint work with Yu Zhou.

Link: https://unipd.zoom.us/j/82518660070?pwd=RUpxL1FnZG9yVzFrOCtrM0xYMEZaZz09

Meeting ID: 825 1866 0070

Password: 62542