Cotilting Sheaves over Weighted Noncommutative Regular Projective Curves

摘要

We consider the category (mathrm{Qcoh},mathbb{X}) of quasicoherent sheaves where (mathbb{X}) is a weighted noncommutative regular projective curve over a field (k). This category is a hereditary, locally noetherian Grothendieck category. We classify all indecomposable pure-injective sheaves and all cotilting sheaves of slope (infty ). In the cases of nonnegative orbifold Euler characteristic this leads to a classification of pure-injective indecomposable sheaves and a description of all large cotilting sheaves in (mathrm{Qcoh},mathbb{X}).