本文選題：Tame核　切入點(diǎn)：純五次數(shù)域　出處：《南京師范大學(xué)》2017年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：本文主要研究了純五次數(shù)域的素理想分解,Eisenstein型純五次數(shù)域的理想類(lèi)群和類(lèi)數(shù)以及純五次數(shù)域的Tame核的2-rank和q-rank( 為奇素?cái)?shù)).第一章主要介紹了本文需要用到的預(yù)備知識(shí),研究背景和主要結(jié)論.假設(shè)則F是純五次數(shù)域.在第二章中,主要研究了純五次數(shù)域F的素理想分解及Eisenstein型純五次數(shù)域的理想類(lèi)群Cl(OF)和類(lèi)數(shù)h(F).假設(shè)g是奇素?cái)?shù),ζq是q次本原單位根,令E=F(ζq),則Gal(E/F)=Gal(Q((q)/Q).第三章主要研究了純五次數(shù)域Tame核的2-rank及q-rank,給出了下面兩個(gè)主要結(jié)論:Ⅰ:(1)若F是純五次域,即Q, m為正整數(shù)時(shí),有其中(2)若F是純五次域,即Q, m為正整數(shù),E=F(ζ5),則或Ⅱ:假設(shè)F是純五次域,即Q, m為正整數(shù),若E=F(ζq),AE是Cl(OE)的g - sylow子群,則(1)當(dāng) 時(shí)(2)當(dāng) g = 5,(g,m) = 1 時(shí),(a)若 m4 三 1 (mod 25)時(shí),則5-rank K2OF 5-rank ε3AE + 1;(b)若m4 (?) 1(mod25)時(shí),則5-rank K2OF = 5-rank ε3AE·(3)當(dāng)(g,m) ≠ 1,qa‖m, (5, a) = 1 時(shí),則q-rank K2OF = q-rank εq-2AE·特別地,當(dāng)時(shí),其中p1,p2, p3, p4為不等于5的互不相同的素?cái)?shù),1≤a ≤ 4,我們具體的得到了 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，

本文編號(hào)：1588887