Automorphism group of the projective line $\mathbb{P}^1(\mathbb{Z})$

Asked May 06 '22 at 13:22

Active May 06 '22 at 13:42

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Consider ``the'' projective line over the integers (which can come in various guises). I have two questions:

What is the scheme-theoretic automorphism group of the scheme $\texttt{Proj}(\mathbb{Z}[x, y])$ ?
What is the automorphism group of $\mathbb{P}^1(\mathbb{Z})$ seen as a projective line over a ring (with typical coordinates, similar to the vector-spacial definition) ?

edited May 06 '22 at 13:42

asked May 06 '22 at 13:22

Boccherini

1

Please don't write $\mathbb{P}^1 (\mathbb{Z})$ for the scheme. (It usually denotes the set of $\mathbb{Z}$-valued points of $\mathbb{P}^1$.) – Zhen Lin May 06 '22 at 13:28
@reuns: oops, a typo, I'll change it right away. – Boccherini May 06 '22 at 13:39
@ZhenLin: agreed, I will edit the question. – Boccherini May 06 '22 at 13:40

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