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Certain topologies on the category of schemes (or perhaps certain appropriate subcategories thereof) are named rather aptly, e.g. Zariski, étale, fppf, fpqc, syntomic, smooth, v(aluation), etc., but what about the more exotic ones like the h-topology or the arc topology ? What are their stories ?

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    $\begingroup$ The h-topology was introduced by Voevodsky in 1990s. I suspect "h" stands for homotopy, but I'm not really sure. $\endgroup$
    – Donu Arapura
    Commented Jun 24, 2022 at 11:43
  • $\begingroup$ The etymology of 'syntomic' is elegant, but not exactly self-explanatory, except to speakers of ancient Greek! $\endgroup$
    – David Loeffler
    Commented Jun 24, 2022 at 12:34
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    $\begingroup$ According to the paper introducing the arc topology, "arc" was chosen by analogy between rank 1 valuations and arcs. I guess they're both segments of curves. $\endgroup$
    – Will Sawin
    Commented Jun 26, 2022 at 15:51
  • $\begingroup$ In general, your best hope for questions of this type is to look at the paper introducing the term. $\endgroup$
    – Will Sawin
    Commented Jun 26, 2022 at 15:52

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