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I am reading a definition saying that an algebraic group over a field $K$ is called a torus if it is isomorphic to product of copies of the multiplicative group $G_m = K^*$. I don't understand why this definition, because $K^*$ is the affine line removing the origin, and it does not look like a circle. Can anyone help me please?

Long
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    The complex points are homotopic to a circle. Anyway, the group is abelian and resembles a torus from the theory of Lie groups. – user40276 Jun 25 '15 at 08:02
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    Related: https://en.wikipedia.org/wiki/Algebraic_torus –  Jun 25 '15 at 08:04

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