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Let $\mathcal{G}$ be a affine algebraic group scheme(may not be reductive) over a scheme $S$. How to define a rational representaion of $\mathcal{G}$ (over $S$)? Is there always a faithful representation?

Please provide references related to these questions.

Let $\mathcal{G}$ be a group scheme(may not be reductive) over a scheme $S$. How to define a rational representaion of $\mathcal{G}$ (over $S$)? Is there always a faithful representation?

Please provide references related to these questions.

Let $\mathcal{G}$ be a affine algebraic group scheme(may not be reductive) over a scheme $S$. How to define a rational representaion of $\mathcal{G}$ (over $S$)? Is there always a faithful representation?

Please provide references related to these questions.

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user100841
user100841

Representation of a group scheme

Let $\mathcal{G}$ be a group scheme(may not be reductive) over a scheme $S$. How to define a rational representaion of $\mathcal{G}$ (over $S$)? Is there always a faithful representation?

Please provide references related to these questions.