The construction of tilting cotorsion pairs for hereditary abelian categories

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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.

Keywords

cotorsion pair / tilting object / hereditary abelian category / coherent sheave / weighted projective line

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