Geodesic
Going-Down Results for Ci -Fields
Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 11-20

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DOI

We search for theorems that, given a ${{C}_{i}}$ -field $K$ and a subfield $k$ of $K$ , allow us to conclude that $k$ is a ${{C}_{j}}$ -field for some $j$ . We give appropriate theorems in the case $\text{case }K=k\left( t \right)$ and $K=k\left( \left( t \right) \right)$ . We then consider the more difficult case where $K/k$ is an algebraic extension. Here we are able to prove some results, and make conjectures. We also point out the connection between these questions and Lang's conjecture on nonreal function fields over a real closed field.
DOI : 10.4153/CMB-2006-002-5
Mots-clés : 12F, 14G, Ci -fields, Lang's Conjecture 
Bevelacqua, Anthony J.; Motley, Mark J. Going-Down Results for Ci -Fields. Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 11-20. doi: 10.4153/CMB-2006-002-5
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     title = {Going-Down {Results} for {Ci} {-Fields}},
     journal = {Canadian mathematical bulletin},
     pages = {11--20},
     year = {2006},
     volume = {49},
     number = {1},
     doi = {10.4153/CMB-2006-002-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-002-5/}
}
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