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arXiv · 1110.5076

The dimension of the space of R-places of certain rational function fields

T. Banakh·Ya. Kholyavka·K. Kuhlmann·M. Machura·O. Potyatynyk
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Abstract

We prove that the space $M(K(x,y))$ of $\mathbb R$-places of the field $K(x,y)$ of rational functions of two variables with coefficients in a totally Archimedean field $K$ has covering and integral dimensions $\dim M(K(x,y))=\dim_\IZ M(K(x,y))=2$ and the cohomological dimension $\dim_G M(K(x,y))=1$ for any Abelian 2-divisible coefficient group $G$.

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BibTeXRIS

T. Banakh, Ya. Kholyavka, K. Kuhlmann, M. Machura, O. Potyatynyk. 2011-10-23. The dimension of the space of R-places of certain rational function fields. https://doi.org/10.2478/s11533-014-0409-y

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