The paper proves that in extended module categories, tilting pairs, torsion pairs, and silting complexes are in one-to-one correspondence.
Support $\tau_2$-tilting and 2-torsion pairs
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The theory of $\tau$-tilting was introduced by Adachi--Iyama--Reiten; one of the main results is a bijection between support $\tau$-tilting modules and torsion classes. We are able to generalise this result in the context of the higher Auslander--Reiten theory of Iyama. For a finite-dimensional algebra $A$ with 2-cluster-tilting subcategory $\mathcal{C}\subseteq\mathrm{mod}A$, we are able to find a correspondence between support $\tau_2$-tilting $A$-modules and torsion pairs in $\mathcal{C}$ satisfying an additional functorial finiteness condition.
fields
math.RT 1years
2024 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Tilting theory for extended module categories
The paper proves that in extended module categories, tilting pairs, torsion pairs, and silting complexes are in one-to-one correspondence.