Embedding theorems for spaces of ℝ-places of rational function fields and their products

Katarzyna Kuhlmann, and Franz-Viktor Kuhlmann. "Embedding theorems for spaces of ℝ-places of rational function fields and their products." Fundamenta Mathematicae 218.2 (2012): 121-149. <http://eudml.org/doc/282634>.

@article{KatarzynaKuhlmann2012,
abstract = {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.},
author = {Katarzyna Kuhlmann, Franz-Viktor Kuhlmann},
journal = {Fundamenta Mathematicae},
keywords = {real place; spaces of real places; spaces of orderings; cut; spaces of cuts},
language = {eng},
number = {2},
pages = {121-149},
title = {Embedding theorems for spaces of ℝ-places of rational function fields and their products},
url = {http://eudml.org/doc/282634},
volume = {218},
year = {2012},
}

TY - JOUR
AU - Katarzyna Kuhlmann
AU - Franz-Viktor Kuhlmann
TI - Embedding theorems for spaces of ℝ-places of rational function fields and their products
JO - Fundamenta Mathematicae
PY - 2012
VL - 218
IS - 2
SP - 121
EP - 149
AB - 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.
LA - eng
KW - real place; spaces of real places; spaces of orderings; cut; spaces of cuts
UR - http://eudml.org/doc/282634
ER -