On the torsion in K_2 of a field  

作　　者：XU KeJian & LIU Min College of Mathematics,Qingdao University,Qingdao 266071,China 

出　　处：《Science China Mathematics》2008年第7期1187-1195,共9页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No.10371061)

摘　　要：For a field F,let Gn(F) = {{a,Φn(a)} ∈ K2(F) | a,Φn(a) ∈ F*},where Φn(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 Gn(F) is not a subgroup of K2(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.For a field F,let Gn(F) = {{a,Φn(a)} ∈ K2(F) | a,Φn(a) ∈ F*},where Φn(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 Gn(F) is not a subgroup of K2(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.

关 键 词：NUMBER FIELD function FIELD TORSION Milnor K2-group Mordell CONJECTURE 

分 类 号：O152[理学—数学] O156[理学—基础数学]