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A bestiary of topologies on Sch

The basic answer is essentially as Emerton described in the comment. The most commonly used topologies on schemes are Zariski, Nisnevich, étale, smooth, syntomic, fppf, and fpqc, and this list is tot …
S. Carnahan's user avatar
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Stack associated to Groupoid object in category $\text{Sch}/S$

For any algebraic stack $X$, there is a groupoid in schemes whose fppf stackification is equivalent to $X$. You can construct such a groupoid following the stacks project, by choosing a smooth presen …
S. Carnahan's user avatar
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