2025/03/28 by Chen, Mingfa
#Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.22217
This paper presents a precise relationship between semi-orthogonal decompositions (SOD) and finite t-stabilities on a triangulated category D. By means of a reduction method to certain quotient categories, we provide a characterization of the connectedness of the mutation graph of the finest ∞-admissible SODs of D. Moreover, when D admits a Serre functor and satisfies a mild condition, we show one-to-one correspondences among (1) finest SODs, (2) finite finest t-stabilities, (3) finite finest admissible filtrations, and (4) full exceptional sequences. These correspondences are proved to be compatible with mutations. As applications, we obtain a classification of SODs for the projective plane, weighted projective lines, and finite acyclic quivers via the t-stability approach.