Buchweitz, Ragnar-Olaf; Leuschke, Graham J.; Van den Bergh, Michel On the derived category of Grassmannians in arbitrary characteristic. (English) Zbl 1333.14017 Compos. Math. 151, No. 7, 1242-1264 (2015). Let \(\mathcal{T}\) be an algebraic triangulated category. An object \(T \in \mathcal{T}\) is called a tilting object if it classically generates the triangulated category and its Ext-algebra is concentrated in degree zero. Under certain finiteness assumptions tilting objects lead to equivalences to derived categories of modules. A sequence of objects \(E_1, \dots, E_n \in \mathcal{T}\) is called an exceptional sequence if they classically generate \(\mathcal{T}\) and there are no nonzero morphisms from \(E_i\) to \(E_j[k]\) for any \(j > i\) and any integer \(k \in \mathbb{Z}\).In the paper under review the authors generalise classical results of M. Kapranov [Invent. Math. 92, No. 3, 479–508 (1988; Zbl 0651.18008)] about tilting objects and exceptional collections in the bounded derived category of coherent sheaves on Grassmannians to fields of arbitrary characteristic. Reviewer: Lennart Galinat (Köln) Cited in 1 ReviewCited in 14 Documents MSC: 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 14M15 Grassmannians, Schubert varieties, flag manifolds 16S38 Rings arising from noncommutative algebraic geometry 15A75 Exterior algebra, Grassmann algebras Keywords:Grassmannian variety; exceptional collection; tilting bundle; semi-orthogonal decomposition; quasi-hereditary algebra Citations:Zbl 0651.18008 PDFBibTeX XMLCite \textit{R.-O. Buchweitz} et al., Compos. Math. 151, No. 7, 1242--1264 (2015; Zbl 1333.14017) Full Text: DOI arXiv References: [1] doi:10.2307/1970952 · Zbl 0327.14016 · doi:10.2307/1970952 [2] doi:10.1007/BF00533374 · Zbl 0705.14007 · doi:10.1007/BF00533374 [3] doi:10.1007/s10468-007-9080-3 · Zbl 1148.14010 · doi:10.1007/s10468-007-9080-3 [5] doi:10.1017/CBO9780511661853.007 · doi:10.1017/CBO9780511661853.007 [6] doi:10.1002/mana.19981910109 · Zbl 0957.14035 · doi:10.1002/mana.19981910109 [9] doi:10.1007/BF01215476 · Zbl 0537.14029 · doi:10.1007/BF01215476 [10] doi:10.1007/978-94-017-1556-0_7 · doi:10.1007/978-94-017-1556-0_7 [11] doi:10.1093/qmath/44.1.17 · Zbl 0832.16011 · doi:10.1093/qmath/44.1.17 [13] doi:10.1007/978-3-540-89394-3 · doi:10.1007/978-3-540-89394-3 [14] doi:10.1007/BF02571640 · Zbl 0798.20035 · doi:10.1007/BF02571640 [16] doi:10.1007/BF01214334 · Zbl 0455.20029 · doi:10.1007/BF01214334 [19] doi:10.1016/0001-8708(88)90007-2 · Zbl 0659.20035 · doi:10.1016/0001-8708(88)90007-2 [20] doi:10.1017/CBO9780511546556 · doi:10.1017/CBO9780511546556 [22] doi:10.1016/j.jalgebra.2010.03.008 · Zbl 1245.20060 · doi:10.1016/j.jalgebra.2010.03.008 [23] doi:10.1007/BF01393744 · Zbl 0651.18008 · doi:10.1007/BF01393744 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.