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On the derived category of Grassmannians in arbitrary characteristic. (English) Zbl 1333.14017

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.

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

Citations:

Zbl 0651.18008
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References:

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