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ryankeleti / ega

amateur translation project of Grothendieck's EGA.
https://ryankeleti.com/ega
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First draft of section IV.16.5 #156

Closed solov-t closed 4 years ago

solov-t commented 4 years ago

Also created an operator for the space of derivations and its associated sheaf (which will eventually be also necessary on section 0.20).

They call "$G$-torseur" by the name of "torseur sous $G$", which seems to have an english equivalent as "torsor over $G$". Anyway, it seemed more closer to the spirit of this project to leave it as "torsor over $G$" even though the first term seems standard nowadays since we're calling "schemes" "preschemes".

ryankeleti commented 4 years ago

Thank you!

ryankeleti commented 4 years ago

@solov-t On G-torsor: good point---I do think G-torsor is a little more modern / shorter to write, but I agree with your keeping to the source, although I believe the translation should be "torsor under G". I think for a scheme S, "G-torsor over S" = "torsor under G over S".

solov-t commented 4 years ago

Translating literally I believe it would be so too, but I tried to look for some English analogue of this. The closest I could find was on this page which called it torsor 'for' a group G.

(and now I've just realized that I've written torsor over G in the commit, haha. It should've been torsor 'for' G as in the text)

solov-t commented 4 years ago

I'm actually finding some matches for "torsor under G"! Ok, I think I can fix this real quick and make another PR in a sec.

solov-t commented 4 years ago

Oh, you already did that. Thanks!

ryankeleti commented 4 years ago

I found some texts which use the "torsor under G" terminology, so I think it's a safe bet to use it!