Aarhus Universitets segl

Silting reduction using generalised concentric twin cotorsion pairs

Erlend Børve (Universität zu Köln)
Onsdag 20. november 2024 16:15–17:15 G3.1 (1532-314)
Mathematics seminar

Given a triangulated category T and a rigid subcategory R, Iyama–Yang put forward a mild technical condition that lets us compute the Verdier quotient T/thick(R). There are good reasons to extend Iyama–Yang's work to extriangulated categories, but one has to grapple with a more complicated theory of localisation. In this talk, we propose a generalisation of Iyama–Yang's work. More precisely, given an extriangulated category C and a rigid subcategory R giving rise to a generalised concentric twin cotorsion pair, we show that the Verdier quotient C/thick(R) can be expressed as an ideal quotient. If C is 0-Auslander, in the sense of Gorsky–Nakaoka–Palu, it suffices that C admits Bongartz completions. Moreover, the Verdier quotient C/thick(R) then remains 0-Auslander. The talk will be based on Section 5 in arXiv:2405.00593.

Organiseret af: AarHomAlg
Kontakt: Amit Shah Revideret: 26.10.2024