Geodesic
Large Tilting Sheaves over Weighted Noncommutative Regular Projective Curves
Documenta mathematica, Tome 22 (2017), pp. 67-134.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $\Bbb X$ be a weighted noncommutative regular projective curve over a field $k$. The category Qcoh $\Bbb X$ 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.
Classification : 14A22, 18E15, 14H45, 14H52, 16G70
Keywords: 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, tube, large sheaf, recollement of triangulated category 
@article{DOCMA_2017__22__a49,
     author = {Angeleri H\"ugel, Lidia and Kussin, Dirk},
     title = {Large {Tilting} {Sheaves} over {Weighted} {Noncommutative} {Regular} {Projective} {Curves}},
     journal = {Documenta mathematica},
     pages = {67--134},
     publisher = {mathdoc},
     volume = {22},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a49/}
}
TY  - JOUR
AU  - Angeleri Hügel, Lidia
AU  - Kussin, Dirk
TI  - Large Tilting Sheaves over Weighted Noncommutative Regular Projective Curves
JO  - Documenta mathematica
PY  - 2017
SP  - 67
EP  - 134
VL  - 22
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a49/
LA  - en
ID  - DOCMA_2017__22__a49
ER  - 
%0 Journal Article
%A Angeleri Hügel, Lidia
%A Kussin, Dirk
%T Large Tilting Sheaves over Weighted Noncommutative Regular Projective Curves
%J Documenta mathematica
%D 2017
%P 67-134
%V 22
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a49/
%G en
%F DOCMA_2017__22__a49
Angeleri Hügel, Lidia; Kussin, Dirk. Large Tilting Sheaves over Weighted Noncommutative Regular Projective Curves. Documenta mathematica, Tome 22 (2017), pp. 67-134. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a49/