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arXiv · 1712.08899

Zariski locality of quasi-coherent sheaves associated with tilting

Michal Hrbek·Jan Šťovíček·Jan Trlifaj
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Abstract

A classic result by Raynaud and Gruson says that the notion of an (infinite dimensional) vector bundle is Zariski local. This result may be viewed as a particular instance (for n = 0) of the locality of more general notions of quasi-coherent sheaves related to (infinite dimensional) n-tilting modules and classes. Here, we prove the latter locality for all n and all schemes. We also prove that the notion of a tilting module descends along arbitrary faithfully flat ring morphisms in several particular cases (including the case when the base ring is noetherian).

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Michal Hrbek, Jan Šťovíček, Jan Trlifaj. 2017-12-24. Zariski locality of quasi-coherent sheaves associated with tilting. https://doi.org/10.1512/iumj.2020.69.7987

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