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

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

2011-10-23

arxiv.org/abs/1110.5076v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

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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