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Motives in tropical geometry
Is there a notion of motives in tropical geometry? Similar like the notion introduced by Grothendieck in algebraic geometry.
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Finite generation of motivic cohomology of number fields
Let $F$ be a number field ($F=\mathbb Q$ is fine for my purposes) and let $n\geq2$ be an integer. Is it known whether the first motivic cohomology groups
$$\mathrm H^1(\mathrm{Spec}(F),\mathbb Z(n))$$
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