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Nov 3, 2017 at 21:44 vote accept Wenzhe
Oct 26, 2017 at 12:05 comment added Will Sawin Like with most analogies, some features of the Galois group are clarified by this analogy, while others are obscured. This is a good way to explain why Galois representations are interesting and natural objects (for the same reason ODE's are interesting and natural, basically) and to describe the relation of the Galois groups to its inertia groups (they generate it, but other than that the structure is quite complicated) but it's not a very good way to understand technical issues like $p$-adic Hodge theory and the Fontaine-Mazur conjecture.
Oct 26, 2017 at 11:35 history edited Daniel Loughran CC BY-SA 3.0
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Oct 26, 2017 at 11:05 history edited Daniel Loughran CC BY-SA 3.0
added 94 characters in body
Oct 26, 2017 at 10:59 history answered Daniel Loughran CC BY-SA 3.0