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Let $X$ a affine algebraic variety. Then $X$ can have infinite automorphism group, for example $X=\mathbb{A}^1$. Let $G$ be a divisible abelian group. My question is about some condition in $G$ such that I can guarantee the existence of a algebraic variety $X$ such that $G$ is a subgroup of the isomorphism group of $X$.

More specifically, let $G_p$ the $p$-primary component of $G$. I want to construct $X$ with a rational point $P$ such that the orbit of $P$ by $G_p$ is rational over $\mathbb{Z}_p$. I want to know if there is some bibliography about this problem?.

Let $X$ a affine algebraic variety. Then $X$ can have infinite automorphism group, for example $X=\mathbb{A}^1$. Let $G$ be a divisible abelian group. My question is about some condition in $G$ such that I can guarantee the existence of a algebraic variety $X$ such that $G$ is a subgroup of the isomorphism group of $X$.

More specifically, let $G_p$ the $p$-primary component of $G$. I want to construct $X$ with a rational point $P$ such that the orbit of $P$ by $G_p$ is rational over $\mathbb{Z}_p$. I want to know if there is some bibliography about this problem?.

Let $X$ a affine algebraic variety. Then $X$ can have infinite automorphism group, for example $X=\mathbb{A}^1$. Let $G$ be a divisible abelian group. My question is about some condition in $G$ such that I can guarantee the existence of a algebraic variety $X$ such that $G$ is a subgroup of the isomorphism group of $X$.

More specifically, let $G_p$ the $p$-primary component of $G$. I want to construct $X$ with a rational point $P$ such that the orbit of $P$ by $G_p$ is rational over $\mathbb{Z}_p$. I want to know if there is some bibliography about this problem.

corrected wrong wording
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YCor
YCor
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Divisible group as the isomorphismautomorphism group of a algebraic variety?

Let $X$ a affine algebraic variety. We have thatThen $X$ can have infinite isomorphismsautomorphism group, for example let $X=\mathbb{A}^1$. Let $G$ be a divisible abelian group. My question is about some condition in $G$ such that I can garantizeguarantee the existence of a algebraic variety $X$ such that $G$ is a subgroup of the isomorphism group of $X$.

More specifically, let $G_p$ the $p$-primary component of $G$. I want to construct $X$ with a rational point $P$ such that the orbiteorbit of $P$ by $G_p$ is rational over $\mathbb{Z}_p$. I want to know if there is some bibliography about itthis problem?.

Divisible group as the isomorphism group of a algebraic variety?

Let $X$ a affine algebraic variety. We have that $X$ can have infinite isomorphisms, for example let $X=\mathbb{A}^1$. Let $G$ be a divisible group. My question is about some condition in $G$ such that I can garantize the existence of a algebraic variety $X$ such that $G$ is a subgroup of the isomorphism group of $X$.

More specifically let $G_p$ the $p$-primary component of $G$. I want to construct $X$ with a rational point $P$ such that the orbite of $P$ by $G_p$ is rational over $\mathbb{Z}_p$. I want to know if there is some bibliography about it problem?.

Divisible group as the automorphism group of a algebraic variety?

Let $X$ a affine algebraic variety. Then $X$ can have infinite automorphism group, for example $X=\mathbb{A}^1$. Let $G$ be a divisible abelian group. My question is about some condition in $G$ such that I can guarantee the existence of a algebraic variety $X$ such that $G$ is a subgroup of the isomorphism group of $X$.

More specifically, let $G_p$ the $p$-primary component of $G$. I want to construct $X$ with a rational point $P$ such that the orbit of $P$ by $G_p$ is rational over $\mathbb{Z}_p$. I want to know if there is some bibliography about this problem?.

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camilo
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Divisible group as the isomorphism group of a algebraic variety?

Let $X$ a affine algebraic variety. We have that $X$ can have infinite isomorphisms, for example let $X=\mathbb{A}^1$. Let $G$ be a divisible group. My question is about some condition in $G$ such that I can garantize the existence of a algebraic variety $X$ such that $G$ is a subgroup of the isomorphism group of $X$.

More specifically let $G_p$ the $p$-primary component of $G$. I want to construct $X$ with a rational point $P$ such that the orbite of $P$ by $G_p$ is rational over $\mathbb{Z}_p$. I want to know if there is some bibliography about it problem?.