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YCor
YCor
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Reference Request: Anisotropic Algebraic Groups Have No Unipotent Elementsalgebraic groups have no unipotent elements

I have found the following fact stated in a number of places:

If $k$ is any field, a connected reductive group $G$ is anisotropic if and only if its only unipotent element is $e$ and $\mathrm{Hom}_k(G, \mathrm{G}_m)$ is trivial.

For instance, this appears in sectionSection 3.4 of Springer's Corvallis article. However, I have been unable to track down a reference for a proof of this result.

Reference Request: Anisotropic Algebraic Groups Have No Unipotent Elements

I have found the following fact stated in a number of places:

If $k$ is any field, a connected reductive group $G$ is anisotropic if and only if its only unipotent element is $e$ and $\mathrm{Hom}_k(G, \mathrm{G}_m)$ is trivial.

For instance, this appears in section 3.4 of Springer's Corvallis article. However, I have been unable to track down a reference for a proof of this result.

Anisotropic algebraic groups have no unipotent elements

I have found the following fact stated in a number of places:

If $k$ is any field, a connected reductive group $G$ is anisotropic if and only if its only unipotent element is $e$ and $\mathrm{Hom}_k(G, \mathrm{G}_m)$ is trivial.

For instance, this appears in Section 3.4 of Springer's Corvallis article. However, I have been unable to track down a reference for a proof of this result.

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GH from MO
GH from MO
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Alexander
Alexander
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Reference Request: Anisotropic Algebraic Groups Have No Unipotent Elements

I have found the following fact stated in a number of places:

If $k$ is any field, a connected reductive group $G$ is anisotropic if and only if its only unipotent element is $e$ and $\mathrm{Hom}_k(G, \mathrm{G}_m)$ is trivial.

For instance, this appears in section 3.4 of Springer's Corvallis article. However, I have been unable to track down a reference for a proof of this result.