Let be a weighted noncommutative regular projective curve over a field . The category Qcoh of quasicoherent sheaves is a hereditary, locally noetherian Grothendieck category. We classify all tilting sheaves which have a non-coherent torsion subsheaf. In case of nonnegative orbifold Euler characteristic we classify all large (that is, non-coherent) tilting sheaves and the corresponding resolving classes. In particular we show that in the elliptic and in the tubular cases every large tilting sheaf has a well-defined slope.
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Lidia Angeleri Hügel, Dirk Kussin, Large Tilting Sheaves over Weighted Noncommutative Regular Projective Curves. Doc. Math. 22 (2017), pp. 67–134DOI 10.4171/DM/560