We study spaces M(R(y)) of ℝ-places of rational function fields R(y) in one variable. For extensions F|R of formally real fields, with R real closed and satisfying a natural condition, we find embeddings of M(R(y)) in M(F(y)) and prove uniqueness results. Further, we study embeddings of products of spaces of the form M(F(y)) in spaces of ℝ-places of rational function fields in several variables. Our results uncover rather unexpected obstacles to a positive solution of the open question whether the torus can be realized as a space of ℝ-places.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-2-2,
author = {Katarzyna Kuhlmann and Franz-Viktor Kuhlmann},
title = {Embedding theorems for spaces of $\mathbb{R}$-places of rational function fields and their products},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {121-149},
zbl = {1262.12002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-2-2}
}
Katarzyna Kuhlmann; Franz-Viktor Kuhlmann. Embedding theorems for spaces of ℝ-places of rational function fields and their products. Fundamenta Mathematicae, Tome 219 (2012) pp. 121-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-2-2/