Timeline for Divisible group as the automorphism group of a algebraic variety?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 14, 2018 at 8:06 | review | Close votes | |||
| Jan 15, 2018 at 13:06 | |||||
| Jan 4, 2018 at 6:31 | review | Close votes | |||
| Jan 5, 2018 at 10:01 | |||||
| Jan 4, 2018 at 2:34 | comment | added | YCor | Sorry, but I don't precisely see the connection to your question. What is the divisible subgroup you are considering? | |
| Jan 4, 2018 at 1:48 | comment | added | camilo | Let $X$ be a algebraic curve over $\mathbb{A}^1$. Suppose that $X=Spec(A)$. Since $A$ is a finite extension of $\mathbb{Z}[T]$ then the automorphism group of $A$ is a semidirect product between a finite group $G$ (the galois group of theextension) by the Automorphism group of $\mathbb{A}^1$. I expect that the last group have a subgroup isomorphic to $\mathbb{Z}$. | |
| Jan 4, 2018 at 1:23 | comment | added | YCor | Yes but I mean the setting sounds vague. I guess you mean $X$ to be defined over $\mathbf{Q}$ (for "rational over $\mathbf{Z}_p$) to make sense. But also I don't even see why a $G_p$-orbit should be a subvariety. If you had an example in mind to illustrate this orbit stuff, it would be useful. | |
| Jan 4, 2018 at 1:17 | history | edited | Qfwfq | CC BY-SA 3.0 |
deleted 1 character in body
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| Jan 4, 2018 at 1:02 | comment | added | camilo | I'm sorry the question was about if there are some bibliography in it direction. | |
| Jan 4, 2018 at 0:06 | comment | added | YCor | I edited to fix wrong wording (I expected you would do so). Still I don't really understand what is the question, if there is any. | |
| Jan 4, 2018 at 0:05 | history | edited | YCor | CC BY-SA 3.0 |
corrected wrong wording
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| Jan 3, 2018 at 17:10 | comment | added | camilo | I'm sorry I want to mean "automorphism". With respect to the second question in principle $G$ is abelian, and the $p$ primary component is the set of elements whose order is a power of $p$. I though in the problem. Let $\tau(G)$ the torsion group of $G$. Maybe if $G/\tau(G)= \mathbb{Q}^n$ then it quotient induce the space $\mathbb{A}^n$ and $\tau(G)$ be the galois group of the variety over $\mathbb{A}^n$. | |
| Jan 3, 2018 at 2:46 | comment | added | YCor | "Divisible group": are you assuming abelian? What is the $p$-primary component? the set of torsion elements whose order is a power of $p$? | |
| Jan 3, 2018 at 2:44 | comment | added | YCor | You're using "isomorphism" instead of "automorphism". The distinction between this two words is precious! Second, "has infinite automorphisms" is senseless. I don't guess if you mean "has an infinite automorphism group" or "has automorphisms of infinite order". | |
| Jan 2, 2018 at 18:35 | history | asked | camilo | CC BY-SA 3.0 |