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Let G and H be affine algebraic groups over a scheme S of characteristic 0 and let \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 be the functor T \mapsto \text{Hom}_{T,gp}(G,H) http://latex.mathoverflow.net/png?T%20%5Cmapsto%20%5Ctext%7BHom%7D%5F%7BT%2Cgp%7D%28G%2CH%29

Theorem (SGA 3, expose XXIV, 7.3.1(a)): Suppose G is reductive. Then \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 is representable by a scheme.

Can this fail if G is not reductive? I worked out a few example with G = \mathbb{G}_a http://latex.mathoverflow.net/png?%5Cmathbb%7BG%7D%5Fa, but they were representable.

Let $G$ and $H$ be affine algebraic groups over a scheme $S$ of characteristic 0 and let $\textbf{Hom}_{S,gp}(G,H)$ be the functor $T \mapsto \text{Hom}\_{T,gp}(G,H)$

Theorem (SGA 3, expose XXIV, 7.3.1(a)): Suppose G is reductive. Then $\textbf{Hom}_{S,gp}(G,H)$ is representable by a scheme.

Can this fail if $G$ is not reductive? I worked out a few example with $G = \mathbb{G}_a$, but they were representable.

Let G and H be affine algebraic groups over a scheme S of characteristic 0 and let \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 be the functor

 T \mapsto \text{Hom}_{T,gp}(G,H) http://latex.mathoverflow.net/png?T%20%5Cmapsto%20%5Ctext%7BHom%7D%5F%7BT%2Cgp%7D%28G%2CH%29

Theorem (SGA 3, expose XXIV, 7.3.1(a)): Suppose G is reductive. Then \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 is representable by a scheme.

Can this fail if G is not reductive? I worked out a few example with G = \mathbb{G}_a http://latex.mathoverflow.net/png?%5Cmathbb%7BG%7D%5Fa, but they were representable.

Let G and H be affine algebraic groups over a scheme S of characteristic 0 and let \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 be the functor  T \mapsto \text{Hom}_{T,gp}(G,H) http://latex.mathoverflow.net/png?T%20%5Cmapsto%20%5Ctext%7BHom%7D%5F%7BT%2Cgp%7D%28G%2CH%29

Theorem (SGA 3, expose XXIV, 7.3.1(a)): Suppose G is reductive. Then \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 is representable by a scheme.

Can this fail if G is not reductive? I worked out a few example with G = \mathbb{G}_a http://latex.mathoverflow.net/png?%5Cmathbb%7BG%7D%5Fa, but they were representable.

Let G and H be affine algebraic groups over a scheme S of characteristic 0 and let \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 be the functor  T \mapsto \text{Hom}_{T,gp}(G,H) http://latex.mathoverflow.net/png?T%20%5Cmapsto%20%5Ctext%7BHom%7D%5F%7BT%2Cgp%7D%28G%2CH%29

Theorem (SGA 3, expose XXIV, 7.3.1(a)): Suppose G is reductive. Then \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 is representable by a scheme.

Can this fail if G is not reductive? I worked out a few example with G = \mathbb{G}_a http://latex.mathoverflow.net/png?%5Cmathbb%7BG%7D%5Fa, but they were representable.

Let G and H be affine algebraic groups over a scheme S of characteristic 0 and let \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 be the functor 

T \mapsto \text{Hom}_{T,gp}(G,H) http://latex.mathoverflow.net/png?T%20%5Cmapsto%20%5Ctext%7BHom%7D%5F%7BT%2Cgp%7D%28G%2CH%29

Theorem (SGA 3, expose XXIV, 7.3.1(a)): Suppose G is reductive. Then \textbf{Hom}_{S,gp}(G,H) http://latex.mathoverflow.net/png?%5Ctextbf%7BHom%7D%5F%7BS%2Cgp%7D%28G%2CH%29 is representable by a scheme.

Can this fail if G is not reductive? I worked out a few example with G = \mathbb{G}_a http://latex.mathoverflow.net/png?%5Cmathbb%7BG%7D%5Fa, but they were representable.