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dim(X) gives wrong answer for X=Spec(A) and A localized at a prime ideal #2639

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afkafkafk13 opened this issue Aug 7, 2023 · 0 comments · Fixed by #2766
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dim(X) gives wrong answer for X=Spec(A) and A localized at a prime ideal #2639

afkafkafk13 opened this issue Aug 7, 2023 · 0 comments · Fixed by #2766
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afkafkafk13 commented Aug 7, 2023

julia> R,(x,y,z) = QQ["x","y","z"];

julia> U=complement_of_prime_ideal(ideal(R,[x,y]));

julia> S,_ = Localization(R,U);

julia> X = Spec(S)
Spectrum
of localization
of multivariate polynomial ring in 3 variables over QQ
at complement of prime ideal(x, y)

julia> dim(X)
3 WRONG

X =Spec(S) and S is clearly a regular local ring of Krull-dimension 2 (as the maximal ideal is generated by 2 elements x and y). so X should have dimension 2.
(Caution: Do not be misled by trdeg_QQ ( Quot(S) ) = 3)

Suggestion for ad hoc fix (to be improved later on): forbid dim for localizations at prime ideals for the time being.

@afkafkafk13 afkafkafk13 added the bug Something isn't working label Aug 7, 2023
paemurru added a commit to paemurru/Oscar.jl that referenced this issue Sep 4, 2023
paemurru added a commit to paemurru/Oscar.jl that referenced this issue Sep 4, 2023
Implemented dimension for localizations along complements of prime
ideals and powers of an element. Not implemented for other
localizations.
@lgoettgens lgoettgens linked a pull request Sep 4, 2023 that will close this issue
simonbrandhorst pushed a commit that referenced this issue Sep 5, 2023
* Fix dim for affine schemes (#2639)

Implemented dimension for localizations along complements of prime
ideals and powers of an element. Not implemented for other
localizations.

---------

Co-authored-by: Matthias Zach <[email protected]>
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