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One answer: the roots of unity in $K$ are precisely the elementsprecisely the elements of $K$ which have absolute value $1$ for every absolute value on $K$; the elements of the constant field have this property for function fields.

One answer: the roots of unity in $K$ are precisely the elements of $K$ which have absolute value $1$ for every absolute value on $K$; the elements of the constant field have this property for function fields.

One answer: the roots of unity in $K$ are precisely the elements of $K$ which have absolute value $1$ for every absolute value on $K$; the elements of the constant field have this property for function fields.

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David E Speyer
David E Speyer
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One answer: the roots of unity in $K$ are precisely the elements of $K$ which have absolute value $1$ for every absolute value on $K$; the elements of the constant field have this property for function fields.