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If I have a reductive algebraic group $G$ defined over a non-archimedean local field $F$. We can define a one-parameter subgroup to be a group homomorphism from $G_{m}$ to $G$. I was wondering, if I have a reductive algebraic group $G$ is there a set of steps that one can follow to find the set of one parameter subgroups of $G$.

Or in general, what are good references to read about this?

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    $\begingroup$ Why not $G_a$ as well? The elliptic case doesn't show up as there are no non-trivial morphisms from a projective to an affine scheme. Well, each of the multiplicative ones sits inside a maximal torus. Of theses there are only finitely many conjugacy classes. Next any additive group sits inside a maximal unipotent subgroup and I am not sure, but there might be only one conjugacy class of those. $\endgroup$ Commented Mar 1, 2024 at 5:15
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    $\begingroup$ These are known as multiplicative cocharacters. Note that they are countably many. (Reductivity of the ambient group plays no role.) $\endgroup$ Commented Mar 1, 2024 at 7:27

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