纯五次数域的Tame核

发布时间：2018-03-09 14:15

  本文选题：Tame核　切入点：纯五次数域　出处：《南京师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文主要研究了纯五次数域的素理想分解,Eisenstein型纯五次数域的理想类群和类数以及纯五次数域的Tame核的2-rank和q-rank( 为奇素数).第一章主要介绍了本文需要用到的预备知识,研究背景和主要结论.假设则F是纯五次数域.在第二章中,主要研究了纯五次数域F的素理想分解及Eisenstein型纯五次数域的理想类群Cl(OF)和类数h(F).假设g是奇素数,ζq是q次本原单位根,令E=F(ζq),则Gal(E/F)=Gal(Q((q)/Q).第三章主要研究了纯五次数域Tame核的2-rank及q-rank,给出了下面两个主要结论:Ⅰ:(1)若F是纯五次域,即Q, m为正整数时,有其中(2)若F是纯五次域,即Q, m为正整数,E=F(ζ5),则或Ⅱ:假设F是纯五次域,即Q, m为正整数,若E=F(ζq),AE是Cl(OE)的g - sylow子群,则(1)当 时(2)当 g = 5,(g,m) = 1 时,(a)若 m4 三 1 (mod 25)时,则5-rank K2OF 5-rank ε3AE + 1;(b)若m4 (?) 1(mod25)时,则5-rank K2OF = 5-rank ε3AE·(3)当(g,m) ≠ 1,qa‖m, (5, a) = 1 时,则q-rank K2OF = q-rank εq-2AE·特别地,当时,其中p1,p2, p3, p4为不等于5的互不相同的素数,1≤a ≤ 4,我们具体的得到了 5-rank K2OF的值.
[Abstract]:In this paper, we mainly study the ideal class groups and class numbers of prime ideal decomposition of Eisenstein type pure five-degree fields and the 2-rank and q-rank( odd prime numbers) of Tame kernels of pure five-degree fields. In Chapter 1, we mainly introduce the preparatory knowledge needed in this paper. Study background and main conclusions. Suppose F is a pure quintic field. In Chapter 2, In this paper, the prime ideal decomposition of pure quintic field F, the ideal class group of Eisenstein type pure quintic field, and the class number hu F are studied. Let g be an odd prime number, and 味 Q be a primitive unit root of order Q. In chapter 3, we mainly study the 2-rank and q-rank of the pure quintic field Tame kernel, and give the following two main conclusions: I: 1) if F is a pure quintic field, where Q, m is a positive integer, there are 2) if F is a pure quintic, That is, Q, m is a positive integer, then, or 鈪，

本文编号：1588887