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

作者：Guo Xuejun^*; Qin Hourong

来源：Journal of K-Theory, 2008, 1(1): 185-192.

DOI：10.1017/is007011017jkt018

• Higher Moore reciprocity law
• Bloch-Lichtenbaum spectral sequence
• Tate-Poitou duality theorem

Let F be a real number field with r(1) real embeddings. In this paper, we prove that the sequence
K-2i(F){2}-> circle plus(p noncomplex) (H) over cap (0)(F-p;Q(2)/Z(2)(i))-> H-0(F;Q(2)/Z(2)(i)) -> 0
is a complex, where (H) over cap (0)(F-p;Q(2)/Z(2)(i)) are the Tate cohomology groups. Moreover if i equivalent to 0, 1, or 2 (mod 4), then it is exact; if i equivalent to 3 (mod 4), then the homology group at the second term of this complex is isomorphic to circle plus(r1)Z/2Z.

• 出版日期2008
• 单位南京大学