# Questions tagged [group-schemes]

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### Are the prime number objects given by the prime numbers?

There is a way to define the notion of prime number in the framework of group theory, thanks to the following observation: Observation: A non-trivial group $G$ is cyclic of prime order iff for any ...
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### Are equivariant perverse sheaves constructible with respect to the orbit stratification?

[Moved here from MSE] Consider a variety $X$ over a field $k$ (complex numbers is fine) with the action of a group scheme $G$, and a $G$-equivariant perverse sheaf $F$ over $X$. Question. Is it true ...
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### Can one embed a group scheme into a locally constant one such that the quotient exists

Let $S$ be a good enough base scheme (say of finite type over an algebraic closed field) and $G\to S$ be a flat group scheme. I want to ask: can we always find a closed embedding $G\to H$ into another ...
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### P-torsion of elliptic curves

Suppose I have an ordinary elliptic curve $E$ over $\overline{\mathbb{F}}_p$. Then its $p$-torsion $E[p]$ is a finite flat group scheme of order $p^2$. My understanding is that it has $p+1$ subgroups ...
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### What exactly is $\underset{n}{\varprojlim} \ \mu_{p^n}$?

Let $k$ be a field of characteristic $p> 0$. Let $\mu_{p^n}$ denote the group scheme $\mu_{p^n}(R) =\{ x \in R: x^{p^n}=1 \}$. Then there are natural maps from $\mu_{p^n}$ to $\mu_{p^{n-1}}$. I'm ...
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### Example of a connected finite group scheme which is not solvable

What would be an example of a connected finite group scheme over a field $k$ that is not solvable? Here $k$ is algebraically closed. Let $\operatorname{GL}_n$ be the general linear group scheme over ...