Geodesic
Large Tilting Sheaves over Weighted Noncommutative Regular Projective Curves
Documenta mathematica, Tome 22 (2017), pp. 67-134
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Let X be a weighted noncommutative regular projective curve over a field k. The category Qcoh X 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.
DOI : 10.4171/dm/560
Classification : 14A22, 14H45, 14H52, 16G70
Mots-clés : tube, weighted noncommutative regular projective curve, tilting sheaf, resolving class, Prüfer sheaf, noncommutative curve of genus zero, domestic curve, tubular curve, noncommutative elliptic curve, slope of quasicoherent sheaf, Grothendieck category, large sheaf, recollement of triangulated category 
@article{10_4171_dm_560,
     author = {Lidia Angeleri H\"ugel and Dirk Kussin},
     title = {Large {Tilting} {Sheaves} over {Weighted} {Noncommutative} {Regular} {Projective} {Curves}},
     journal = {Documenta mathematica},
     pages = {67--134},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/560},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/560/}
}
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Lidia Angeleri Hügel; Dirk Kussin. Large Tilting Sheaves over Weighted Noncommutative Regular Projective Curves. Documenta mathematica, Tome 22 (2017), pp. 67-134. doi: 10.4171/dm/560

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