Wide subcategories are semistable (Q1753981)

Summary: For an arbitrary finite dimensional algebra \(\Lambda\), we prove that any wide subcategory of \(\mathsf{mod} \Lambda\) satisfying a certain finiteness condition is \(\theta\)-semistable for some stability condition \(\theta\). More generally, we show that wide subcategories of \(\mathsf{mod} \Lambda\) associated with two-term presilting complexes of \(\Lambda\) are semistable. This provides a complement for Ingalls-Thomas-type bijections for finite dimensional algebras.