Geodesic
On residually transcendental valued function fields of conics
Glasgow mathematical journal, Tome 38 (1996) no. 2, pp. 137-145

Voir la notice de l'article provenant de la source Cambridge University Press

Let K/Kobe a finitely generated field extension of transcendence degree 1. Let u0 be a valuation of Koand v a valuation of Kextending v0such that the residue field of vis a transcendental extension ofthe residue field k0of vo/such a prolongation vwill be called a residually transcendental prolongation of v0. Byan element with the uniqueness propertyfor (K, v)/(K0, v0) (or more briefly for v/v0)we mean an element / of Khaving u-valuation 0 which satisfies (i) the image of tunder the canonicalhomomorphism from the valuation ring of vonto the residue field of v(henceforth referred to as the v-residue ot t) is transcendental over ko; that is vcoincides with the Gaussian valuation on the subfield K0(t) defined by (ii) vis the only valuation of K (up to equivalence) extending the valuation . 
Khanduja, Sudesh K. On residually transcendental valued function fields of conics. Glasgow mathematical journal, Tome 38 (1996) no. 2, pp. 137-145. doi: 10.1017/S0017089500031360
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