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  1. Science in China Series A: Mathematics
  2. Science in China Series A: Mathematics : Volume 51
  3. Science in China Series A: Mathematics : Volume 51, Issue 7, July 2008
  4. On the torsion in K $_{2}$ of a field
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Science in China Series A: Mathematics : Volume 60
Science in China Series A: Mathematics : Volume 59
Science in China Series A: Mathematics : Volume 58
Science in China Series A: Mathematics : Volume 57
Science in China Series A: Mathematics : Volume 56
Science in China Series A: Mathematics : Volume 55
Science in China Series A: Mathematics : Volume 54
Science in China Series A: Mathematics : Volume 53
Science in China Series A: Mathematics : Volume 52
Science in China Series A: Mathematics : Volume 51
Science in China Series A: Mathematics : Volume 51, Issue 12, December 2008
Science in China Series A: Mathematics : Volume 51, Issue 11, November 2008
Science in China Series A: Mathematics : Volume 51, Issue 10, October 2008
Science in China Series A: Mathematics : Volume 51, Issue 9, September 2008
Science in China Series A: Mathematics : Volume 51, Issue 8, August 2008
Science in China Series A: Mathematics : Volume 51, Issue 7, July 2008
Correlation of zeros of automorphic L-functions
On the structure of Fatou domains
On the torsion in K $_{2}$ of a field
On the value distribution of ƒ + a(ƒ′)$^{ n }$
Pseudo almost periodic solutions to parabolic boundary value inverse problems
Carleman estimates and unique continuation property for the anisotropic differential-operator equations
The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators
The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces
Large-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilities
Existence, uniqueness and ergodicity of Markov branching processes with immigration and instantaneous resurrection
On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models
Some results on 4$^{ m }$2$^{ n }$ designs with clear two-factor interaction components
Two-stage local M-estimation of additive models
Science in China Series A: Mathematics : Volume 51, Issue 6, June 2008
Science in China Series A: Mathematics : Volume 51, Issue 5, May 2008
Science in China Series A: Mathematics : Volume 51, Issue 4, April 2008
Science in China Series A: Mathematics : Volume 51, Issue 3, March 2008
Science in China Series A: Mathematics : Volume 51, Issue 2, February 2008
Science in China Series A: Mathematics : Volume 51, Issue 1, January 2008
Science in China Series A: Mathematics : Volume 50
Science in China Series A: Mathematics : Volume 49
Science in China Series A: Mathematics : Volume 48
Science in China Series A: Mathematics : Volume 47
Science in China Series A: Mathematics : Volume 46
Science in China Series A: Mathematics : Volume 45
Science in China Series A: Mathematics : Volume 44
Science in China Series A: Mathematics : Volume 43
Science in China Series A: Mathematics : Volume 42
Science in China Series A: Mathematics : Volume 41
Science in China Series A: Mathematics : Volume 40

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On the torsion in K $_{2}$ of a field

Content Provider Springer Nature Link
Author Xu, KeJian Liu, Min
Copyright Year 2008
Abstract For a field F, let G $_{ n }$(F) = {{a,Φ$_{ n }$(a)} ∈ K $_{2}$(F) | a,Φ$_{ n }$(a) ∈ F*}, where Φ$_{ n }$(x) is the n-th cyclotomic polynomial. At first, by using Faltings’ theorem on Mordell conjecture it is proved that if F is a number field and if n ≠ 4, 8, 12 is a positive integer having a square factor then G $_{ n }$(F) is not a subgroup of K $_{2}$(F), and then by using the results of Manin, Grauert, Samuel and Li on Mordell conjecture theorem for function fields, a similar result is established for function fields over an algebraically closed field.
Starting Page 1187
Ending Page 1195
Page Count 9
File Format PDF
ISSN 10069283
Journal Science in China Series A: Mathematics
Volume Number 51
Issue Number 7
e-ISSN 18622763
Language English
Publisher SP Science in China Press
Publisher Date 2008-06-21
Publisher Place Heidelberg
Access Restriction Subscribed
Subject Keyword number field function field torsion Milnor K $_{2}$-group Mordell conjecture $K$-theory of global fields Symbols and arithmetic Applications of Mathematics
Content Type Text
Resource Type Article
Subject Mathematics
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