Cotilting Sheaves over Weighted Noncommutative Regular Projective Curves

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} .