AI 中文总结
研究仿射概型上平坦拓扑的单点覆盖在κ-余滤极限下的情况，证明其不封闭，得出对可达平坦层存在更精细拓扑使其仍为层的结论，展现平坦拓扑与其他大拓扑的不同。
AI 中文摘要
我们证明，对于任意正则基数κ，仿射概型上平坦拓扑中的单点覆盖在κ-余滤极限下不封闭。因此，对于每个可达平坦层，存在一个严格更精细的拓扑，使其仍是一个层。平坦拓扑因此与其他大拓扑，如弧拓扑和纯拓扑形成对比。
英文摘要
We prove that singleton covers in the flat topology on affine schemes are not closed under $κ$-cofiltered limits for any regular cardinal $κ$. 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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