Motivic measures and $\mathbb{F}_1$-geometries

Lieven Le Bruyn

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arXiv · 1901.10243

Motivic measures and $\mathbb{F}_1$-geometries

Lieven Le Bruyn

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Abstract

Right adjoints for the forgetful functors on $\lambda$-rings and bi-rings are applied to motivic measures and their zeta functions on the Grothendieck ring of $\mathbb{F}_1$-varieties in the sense of Lorscheid and Lopez-Pena (torified schemes). This leads us to a specific subring of $\mathbb{W}(\mathbb{Z})$, properly containing Almkvist's ring $\mathbb{W}_0(\mathbb{Z})$, which might be a natural receptacle for all local factors of completed zeta functions.

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BibTeX RIS

Lieven Le Bruyn. 2019-01-29. Motivic measures and $\mathbb{F}_1$-geometries. https://arxiv.org/abs/1901.10243

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