@article{Zhu2025, 
author = {Rongmin Zhu and Tiwei Zhao},
title = {The construction of tilting cotorsion pairs for hereditary abelian categories},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {5},
pages = {2719-2735},
keywords = {cotorsion pair, tilting object, hereditary abelian category, coherent sheave, weighted projective line},
url = {https://www.sciopen.com/article/10.3934/era.2025120},
doi = {10.3934/era.2025120},
abstract = {Through tilting objects, we construct complete cotorsion pairs for specific hereditary abelian categories, such as the category of modules that are finitely generated over a finite-dimensional hereditary algebra as well as the category of coherent sheaves over weighted projective lines.  We prove that a complete cotorsion pair exists in the category of coherent sheaves over a weighted projective curve        X   if and only if        X   is a weighted projective line.  We also characterize the canonical tilting cotorsion pair for any weighted projective line and obtain Hovey triples in the category of vector bundles over a weighted projective line.}
}