Embedding theorems for spaces of $\mathbb R$-places of rational function fields and their products
Volume 218 / 2012
Fundamenta Mathematicae 218 (2012), 121-149
MSC: Primary 12J15; Secondary 12J25.
DOI: 10.4064/fm218-2-2
Abstract
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.
