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

作者：Kuhlmann Katarzyna^*; Kuhlmann Franz Viktor

来源：Fundamenta Mathematicae, 2012, 218(2): 121-149.

DOI：10.4064/fm218-2-2

• real place
• spaces of real places
• spaces of orderings
• cut

We study spaces M(R(y)) of R-places of rational function fields R(y) in one variable. For extensions F vertical bar 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.

• 出版日期2012