Is this a bug in schemes?

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mmarco

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Feb 27, 2013, 2:52:34 PM2/27/13
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I have found the following behaviour:


sage: A=AffineSpace(QQ,1)
sage: B=ProjectiveSpace(QQ,2)
sage: h1=A.hom([x,0,1],B)
sage: h2=A.hom([1,0,x],B)
sage: S=h1.glue_along_domains(h2)
sage: S
Scheme obtained by gluing X and Y along U, where
X: Projective Space of dimension 2 over Rational Field
Y: Projective Space of dimension 2 over Rational Field
U: Affine Space of dimension 1 over Rational Field
sage: S.base_scheme()
Spectrum of Integer Ring
sage: S.base_ring()
Integer Ring


Isn't the result supposed to be over the rationals? Or am i missing
something?

Simon King

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Feb 27, 2013, 3:06:50 PM2/27/13
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On 2013-02-27, mmarco <mma...@unizar.es> wrote:
> Isn't the result supposed to be over the rationals? Or am i missing
> something?

And:

sage: S.category()
Category of sets

Isn't this supposed to be in the category of schemes over the rationals?

Cheers,
Simon

Nils Bruin

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Feb 27, 2013, 4:30:24 PM2/27/13
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On Feb 27, 12:06 pm, Simon King <simon.k...@uni-jena.de> wrote:
> On 2013-02-27, mmarco <mma...@unizar.es> wrote:
>
> > Isn't the result supposed to be over the rationals? Or am i missing
> > something?
>
> And:
>
>   sage: S.category()
>   Category of sets

The __init__ is not calling super().__init__ (or whatever the
appropriate spelling is)
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