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Projective Systems on Trees and Valuation Theory

Published online by Cambridge University Press:  20 November 2018

Olav Arnfinn Laudal
Olav Arnfinn Laudal*
Affiliation:
University of Oslo, Oslo, Norway; Syracuse University, Syracuse, New York
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 984 - 1000
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Laudal, O. A., Sur la théorie des limites projectives et inductives, Ann. Sci. Ecole Norm. Sup. 82 (1965), 241–296.Google Scholar
2. Ribenboim, P., Le théorème d* approximation pour les valuations de Krull, Math. Z. 68 (1957), 1–18.Google Scholar
3. Serre, J.-P., Groupe algébriques et corps de classes (Hermann, Paris, 1959).Google Scholar
4. Zariski, O. and Samuel, P., Commutative algebra, Vol. II (Van Nostrand, New York, 1960).10.1007/978-3-662-29244-0CrossRefGoogle Scholar