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Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.

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Orbits of action of the split group of type $F_4$

Let the split group of type $F_4$ act as the automorphism group of the split Albert algebra $A$. Consider the action of $F_4\times \mathbb{G}_m$ on $A$, given by letting $\mathbb{G}_m$ act by scalar m …
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