Abstract
We prove that for every n ∈ ℕ the space M(K(x 1, …, x n ) of ℝ-places of the field K(x 1, …, x n ) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x 1, …, x n )) ≤ n. For n = 2 the space M(K(x 1, x 2)) has covering and integral dimensions dimM(K(x 1, x 2)) = dimℤ M(K(x 1, x 2)) = 2 and the cohomological dimension dim G M(K(x 1, x 2)) = 1 for any Abelian 2-divisible coefficient group G.
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Banakh, T., Kholyavka, Y., Potyatynyk, O. et al. On the dimension of the space of ℝ-places of certain rational function fields. centr.eur.j.math. 12, 1239–1248 (2014). https://doi.org/10.2478/s11533-014-0409-y
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DOI: https://doi.org/10.2478/s11533-014-0409-y