Cotilting sheaves over weighted noncommutative regular projective curves

Autor:	Kussin, Dirk, Laking, Rosanna
Rok vydání:	2019
Předmět:	Mathematics - Representation Theory Mathematics - Algebraic Geometry Mathematics - Category Theory 14A22 18E15 18E30 18E40
Zdroj:	Doc. Math. 25 (2020), 1029-1077
Druh dokumentu:	Working Paper
Popis:	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 $\operatorname{Qcoh}\mathbb{X}$. Comment: 28 pages, 1 figure. v2: Some typos and formulations fixed, abstract slightly changed, extended number 6.12, additional references, more streamlined recapitulation of the geometric setting
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1911.02485 Zobrazit plný text záznamu View this record from Arxiv