25 February 2026 — Verona

From 2-term to d-term silting complexes

Esha Gupta, University of Paris-Saclay

Abstract

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 τ-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.