Timeline for Galois action on étale path torsors
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 23 at 18:10 | answer | added | kindasorta | timeline score: 1 | |
| Mar 23 at 15:19 | comment | added | kindasorta | In your view, $g(p)$ is the path which satisfies $g(p) = g(F_y)pg^{-1}(F_x)$. I guess the point which I find unclear is: if I replace my Galois element acting on $F_y$ by another element, would I still get a path? For example, is $h(F_y)pg^{-1}(F_x)$ a valid etale path for any $g,h\in G_k$? | |
| Mar 23 at 14:31 | comment | added | KristianJS | It might be easier to see what it looks like from the fiber functor perspective. The torsor of etale paths = Isom(F_x, F_y) for the fiber functors F_x, F_y. An iso. is essentially given by maps between the fibers Y_x and Y_y for all covers Y. Given such a map you can act by Gal on both sides and get a new isom. If I didn't make a dumb mistake that's basically the Galois action. Then you can always translate back from fiber functor picture to check what this action corresponds to. | |
| Mar 23 at 14:05 | history | edited | LSpice | CC BY-SA 4.0 |
'etale' -> 'étale'
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| Mar 23 at 13:52 | history | edited | kindasorta | CC BY-SA 4.0 |
added 72 characters in body
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| Mar 23 at 13:40 | history | asked | kindasorta | CC BY-SA 4.0 |