Classification of valuations on surfaces
Received date: 2008-03-21
Revised date: 2008-07-01
Online published: 2009-05-15
许宁 . 曲面上赋值的分类[J]. 中国科学院大学学报, 2009 , 26(3) : 289 -295 . DOI: 10.7523/j.issn.2095-6134.2009.3.001
By letting K be a finitely generated field extension of k and v be a k-valuation of K, we define the height of the valuation. Based on this we obtain the complete classification of valuations on surfaces. In addition, we get the relationship between the valuation and transcendental power series.
Key words： valuation; height; rank; totally ordered group; transcendental power series
[1] Mo ZJ, Lan YZ, Zhao CL. Algebra 2. Beijing: Peking University Press, 1986. 92~107
[2] Endler O. Valuation theory. Berlin, New York: Springer-Verlag, 1972. 81~82
[3] Hartshorne R. Algebraic geometry. New York: Springer-Verlag, 1977. 42~46
[4] Li KZ. First step of algebraic geometry(in Chinese). Beijing:Science Press,2004
[5] Li KZ. Commutative algebra and homological algebra(in Chinese). Beijing:Science Press,1998
[6] Herrera FJ,Olalla MA, Vicente JL. Valuations in fields of power series. Rev Mat Iberoamericana, 2003,19:467~482.arXiv:math/0605225
[7] Olalla-Acosta MA. On the dimension of discrtete valuations of k((X1,…,Xn)). arXiv:math.AC/0011096,15,2000
[8] Li KZ. Automorphism group schemes of finite field extensions. Max-Planck-Institut für Mathematik Preprint Series,2000
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