Embedding theorems for
spaces of $\mathbb R$-places of rational function fields and their products
Fundamenta Mathematicae, Tome 218 (2012) no. 2, pp. 121-149
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We study spaces $M(R(y))$ of $\mathbb R$-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 $\mathbb R$-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 $\mathbb R$-places.
Keywords:
study spaces mathbb r places rational function fields variable extensions formally real fields real closed satisfying natural condition embeddings prove uniqueness results further study embeddings products spaces form spaces mathbb r places rational function fields several variables results uncover rather unexpected obstacles positive solution question whether torus realized space mathbb r places
Affiliations des auteurs :
Katarzyna Kuhlmann 1 ; Franz-Viktor Kuhlmann 2
@article{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},
pages = {121--149},
year = {2012},
volume = {218},
number = {2},
doi = {10.4064/fm218-2-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm218-2-2/}
}
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%0 Journal Article %A Katarzyna Kuhlmann %A Franz-Viktor Kuhlmann %T Embedding theorems for spaces of $\mathbb R$-places of rational function fields and their products %J Fundamenta Mathematicae %D 2012 %P 121-149 %V 218 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/fm218-2-2/ %R 10.4064/fm218-2-2 %G en %F 10_4064_fm218_2_2
Katarzyna Kuhlmann; Franz-Viktor Kuhlmann. Embedding theorems for spaces of $\mathbb R$-places of rational function fields and their products. Fundamenta Mathematicae, Tome 218 (2012) no. 2, pp. 121-149. doi: 10.4064/fm218-2-2
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