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arXiv · 1407.5782

Points in algebraic geometry

Ofer Gabber·Shane Kelly
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Abstract

We give scheme-theoretic descriptions of the category of fibre functors on the categories of sheaves associated to the Zariski, Nisnevich, \'etale, rh, cdh, ldh, eh, qfh, and h topologies on the category of separated schemes of finite type over a separated noetherian base. Combined with a theorem of Deligne on the existence of enough points, this provides an algebro-geometric description of a conservative family of fibre functors on these categories of sheaves. As an example of an application we show direct image along a closed immersion is exact for all these topologies except qfh. The methods are transportable to other categories of sheaves as well.

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Ofer Gabber, Shane Kelly. 2014-07-22. Points in algebraic geometry. https://arxiv.org/abs/1407.5782

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