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?
2026-03-30 12:25:46.1774873546
Why the multiplicative group $G_m$ is called a 1 dimensional torus?
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