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Uniqueness of Moore's higher reciprocity law at the prime 2 for real number fields

Published online by Cambridge University Press:  07 January 2008

Xuejun Guo  and
Hourong Qin
Xuejun Guo
Affiliation:
guox@nju.edu.cnDepartment of Mathematics, Nanjing University, Nanjing 210093, The People's Republic of China guox@nju.edu.cnThe Abdus Salam International Center for Theoretical Physics, Trieste, Italy
Hourong Qin
Affiliation:
hrqin@nju.edu.cnDepartment of Mathematics, Nanjing University, Nanjing 210093, The People's Republic of China
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Abstract

Let F be a real number field with r1 real embeddings. In this paper, we prove that the sequence

is a complex, where are the Tate cohomology groups. Moreover if i ≡ 0, 1, or 2 (mod 4), then it is exact; if i ≡ 3 (mod 4), then the homology group at the second term of this complex is isomorphic to .

Keywords

Moore's reciprocity uniqueness theoremBloch-Lichtenbaum spectral sequenceTate-Poitou duality theorem
Type
Research Article
Information
Journal of K-Theory , Volume 1 , Issue 1 , February 2008 , pp. 185 - 192
Copyright
Copyright © ISOPP 2008

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References

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