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Cotilting sheaves over weighted noncommutative regular projective curves

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Laking,  Rosanna
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Kussin, D., & Laking, R. (2020). Cotilting sheaves over weighted noncommutative regular projective curves. Documenta Mathematica, 25, 1029-1077. doi:10.25537/dm.2020v25.1029-1077.


Cite as: http://hdl.handle.net/21.11116/0000-0007-A1F9-A
Abstract
We consider the category $\operatorname{Qcoh}\mathbb{X}$ 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 $\operatorname{Qcoh}\mathbb{X}$.