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arXiv · 2603.25272

The crisp topology, a refinement of the fpqc topology

Saskia Kern
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Abstract

We introduce the crisp topology for schemes as a refinement of the fpqc topology. This Grothendieck topology uses the new notion of crisp morphisms, which generalise universal injectivity from ring homomorphisms to arbitrary morphisms of schemes. We study basic properties and demonstrate that this topology is well-behaved.

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Saskia Kern. 2026-03-26. The crisp topology, a refinement of the fpqc topology. https://arxiv.org/abs/2603.25272

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