LOCALIZATIONS OF THE HEARTS OF COTORSION PAIRS

LIU, YU

Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 564-583

Résumé

In this article, we study localizations of hearts of cotorsion pairs ($\mathcal{U}, \mathcal{V}$) where $\mathcal{U}$ is rigid on an extriangulated category $\mathcal{B}$. The hearts of such cotorsion pairs are equivalent to the functor categories over the stable category of $\mathcal{U}$ ($\bmod \underline{\mathcal{U}}$). Inspired by Marsh and Palu (Nagoya Math. J. 225(2017), 64–99), we consider the mutation (in the sense of Iyama and Yoshino, Invent. Math. 172(1) (2008), 117–168) of $\mathcal{U}$ that induces a cotorsion pair ($\mathcal{U}^{\prime}, \mathcal{V}^{\prime}$). Generally speaking, the hearts of ($\mathcal{U}, \mathcal{V}$) and ($\mathcal{U}^{\prime}, \mathcal{V}^{\prime}$) are not equivalent to each other, but we will give a generalized pseudo-Morita equivalence between certain localizations of their hearts.

Détail

DOI : 10.1017/S0017089519000284