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Fill in v_adicCompletionComapAlgHom #245

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erdOne
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@erdOne erdOne commented Nov 26, 2024

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@@ -63,8 +63,6 @@ def comap (w : HeightOneSpectrum B) : HeightOneSpectrum A where
isPrime := Ideal.comap_isPrime (algebraMap A B) w.asIdeal
ne_bot := mt Ideal.eq_bot_of_comap_eq_bot w.ne_bot

open scoped algebraMap
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I feel like this only causes trouble (e.g. the show (r : adicCompletion K (comap A w)) = @UniformSpace.Completion.coe' K this r from rfl below) and we don't really use it anyway.

@erdOne erdOne marked this pull request as ready for review November 26, 2024 16:25
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erdOne commented Nov 26, 2024

This closes #234 #235 and #236


-- this name is surely wrong
open WithZeroTopology in
lemma v_adicCompletionComapAlgHom
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This is the right name according to the naming convention.
We could probably rename adicCompletionComapAlgHom to adicCompletionComap.

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@kbuzzard kbuzzard Nov 30, 2024

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I am totally confused by your comment. How can w(x)=v(x)^e be called v_adicCompletionComapAlgHom? Where's the AlgHom in the statement?

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Your statement does not typecheck because $w$ is a valuation on $\hat{L}$ while $v$ is a valuation on $\hat{K}$.
So the statement is $w(f(x)) = v(x)^e$ where $f : \hat{K} \to \hat{L}$ is the map you called adicCompletionComap

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Fair enough!

@kbuzzard kbuzzard merged commit add5464 into ImperialCollegeLondon:main Dec 1, 2024
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kbuzzard commented Dec 1, 2024

Thanks!

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2 participants