Geodesic
Projective Systems on Trees and Valuation Theory
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 984-1000

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

It is our aim in this note to introduce methods from homological algebra in the study of some problems in valuation theory. In particular, we will use such methods to give a new, and, in some respect, simpler proof of a well-known theorem of Krull and Ribenboim; see (2). We shall also show that the same methods can be used to prove the Riemann-Roch theorem for algebraic curves and the Weierstrass product theorem. 
Laudal, Olav Arnfinn. Projective Systems on Trees and Valuation Theory. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 984-1000. doi: 10.4153/CJM-1968-096-x
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[1] 1. Laudal, O. A., Sur la théorie des limites projectives et inductives, Ann. Sci. Ecole Norm. Sup. 82 (1965), 241–296. Google Scholar

[2] 2. Ribenboim, P., Le théorème d* approximation pour les valuations de Krull, Math. Z. 68 (1957), 1–18. Google Scholar

[3] 3. Serre, J.-P., Groupe algébriques et corps de classes (Hermann, Paris, 1959). Google Scholar

[4] 4. Zariski, O. and Samuel, P., Commutative algebra, Vol. II (Van Nostrand, New York, 1960).10.1007/978-3-662-29244-0 Google Scholar | DOI

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