Comparison of topologies

On music, computing and math

Last year I made a graph comparing a bunch of Grothendieck topologies, and I had been toying with the idea of making an interactive web version of it. Two weeks ago Shane Kelly published a preprint Points in algebraic geometry, while Stefan Schroër tackled in a preprint that appeared on the same day the intriguingly hard case of Points in the fppf topology.

The article by Kelly contains a comparison graph, just like the one I made last year (mine emphasised the « usual » topologies more, and had less topologies), but also describes what type of rings act as stalks for this topology, and gave short definitions of each of the topologies in use. Hence I had all the data to make a complete comparison!

There is a very preliminary draft available. I’ll be away from the internet for 2 weeks, hence if you are looking for a…

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