Higher relative class number formulae
Higher relative class number formulae
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较高相对类别数公式
DOI：
10.1007/s002080200321
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发表时间：
2002
影响因子：
1.4
通讯作者：
M. Kolster
中科院分区：
文献类型：
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作者：
M. Kolster
令 E 为具有最大实子域 F 的全复阿贝尔数域，令 表示 的非平凡特征。与经典的 casen=1 相似，odd 的 ArtinL 函数的值由以下形式的相对类数公式给出：这里 $r_1 = [F:{\Bbb Q}], w_n(E) = |H^0(E,{\Bbb Q}/{\Bbb Z}(n))|，Q_n$ 是较高的 Q 索引，等于 1 或 2，并且是较高的相对类数。这里对于任何数域L，较高类数是有限群$H^2(o_L,{\Bbb Z}(n)):= \prod_p H^2_{\et}(spec o_L[1/p],{\Bbb Z}p(n))的阶，$与L中整数环的较高K理论群的阶密切相关。
LetEbe a totally complex abelian number field with maximal real subfieldF, and letdenote the non-trivial character of. Similar to the classical casen=1 the value of the ArtinL-functionatfor oddis given by a relative class number formula of the formHere $r_1 = [F:{\Bbb Q}], w_n(E) = |H^0(E,{\Bbb Q}/{\Bbb Z}(n))|, Q_n$ is a higherQ-index, which is equal to 1 or 2 andis a higher relative class number. Here for any number fieldLthe higher class numberis the order of the finite group$H^2(o_L,{\Bbb Z}(n)):= \prod_p H^2_{\et}(spec o_L[1/p],{\Bbb Z}p(n)),$closely related to the order of the higherK-theory groupof the ring of integersinL.