Does a connected finite locally free group scheme G over a scheme S of characteristic p>0 has degree a power of p? I know that when S is the spectrum of a field k, it is true. So …

This is a continuation of my question http://mathoverflow.net/questions/16261/. Let $G$ be a smooth, connected, reductive $k$-group over a field $k$ of characteristic $p>0$. Let $ …

Hi, I am trying to define an exponential map for finite abelian group schemes. The following looks like it should work, but doesn't (see below). I am putting up this question hopi …

While the common approach to algebraic groups is via representable functors, it seems that there is no such for differential algebraic groups (defined by differential polynomials). …

By M. Kisin, let $k$ be an algebraically closed field of characteristic $p$, and $K$ be a totally ramified extension of $B(k)$, the fraction field of the Witt vector ring $W(k)$, t …

Let's work over a trait $S=\mathrm{Spec}R$, where $R$ is a dvr with fraction field $K$, residue field $k$. Given an abelian variety $A_K$ with semi-stable reduction, let $A$ over $ …

I am trying to understand some things related to elliptic curves and finite flat group schemes but I am a little bit confused. Let $A$ be a supersingular elliptic curve over an al …

I am looking for reference or hints how to prove the following result. Let $G$ be a commutative $S$-group scheme which is the extension of an abelian scheme $A$ by a torus $T$ …

It is a standard and important fact that any smooth affine group scheme $G$ over a field $k$ is a closed $k$-subgroup of ${\rm{GL}}_n$ for some $n > 0$. (Smoothness can be relaxed …

The structure of a commutative affine algebraic group $G$ over a field $k$ is understood (SGA 3): $G$ has a maximal subgroup of multiplicative type $M$ and the quotient $G/M$ is un …

Can you tell me, where I can find a proof of the following fact: Let $R$ be a commutative ring. Consider the category of commutative Hopf algebras over $R$. Then this category is e …

Let $\pi: G \rightarrow S$ be a finite flat group scheme over a locally noetherian connected base scheme $S$. Its degree is defined as the rank of the locally free $\mathcal O_S$-m …

A Lie group can (often) be recovered as the $\mathbb{R}$-points of a group scheme. I am wondering if this parallelism carries over to proper actions. In particular, let $G$ be a L …

Can I have some examples of finite non-commutative connected group schemes over a field $k$? I would like also to see some non-trivial torsors over a $k$-scheme $X$ under such gr …

Let $p$ be a prime number and $R$ be a Noetherian local ring of characteristic $p$ with residue field $k$. Let $G$ be a finite etale subgroup scheme over $R$ of order $p$. Suppose …