Cotilting Sheaves over Weighted Noncommutative Regular Projective Curves
Doc. Math. 25, 1029-1077 (2020)
DOI: 10.25537/dm.2020v25.1029-1077
Communicated by Henning Krause
Summary
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 \(\mathrm{Qcoh}\,\mathbb{X}\).
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Affiliation
Kussin, Dirk
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
Laking, Rosanna
Università degli Studi di Verona, Strada Le Grazie 15 - Ca' Vignal 2, I-37134 Verona, Italy
