Re: Irreducible constant dimensional fibres --> irreducibility?

ulfarsson in litteris
<92eee148-587d-4899-aa2d-9c9892549c5d@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
scripsit:
On Dec 11, 2:31 pm, david.mad...@xxxxxx (David Madore) wrote:
No. Let Y be the affine line, let X be the disjoint union of {0} in Y
and its (open) complement.

@David: Your X will fail to be affine - I think. Please correct me
if I'm wrong!

It is affine:

* {0} is certainly affine (it is Spec k),

* its complement in Y is also affine (it is G_m = Spec k[t, t^{-1}] =
Spec k[u,v]/(uv-1)),

* the disjoint union of two affine schemes is again affine (Spec A +
Spec B = Spec (A*B)).

So X is the spectrum of k * k[t,t^{-1}].

--
David A. Madore
(david.madore@xxxxxx,
http://www.madore.org/~david/ )

.

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