Inaccessibility of the flat topology

Ko Aoki; Robert Burklund

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arXiv · 2607.09440

Inaccessibility of the flat topology

Ko Aoki·Robert Burklund

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Abstract

We prove that singleton covers in the flat topology on affine schemes are not closed under $\kappa$-cofiltered limits for any regular cardinal $\kappa$. Therefore, for every accessible flat sheaf there exists a strictly finer topology for which it is still a sheaf. The flat topology thus contrasts with other big topologies, such as the arc and pure topologies.

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Ko Aoki, Robert Burklund. 2026-07-10. Inaccessibility of the flat topology. https://arxiv.org/abs/2607.09440

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