博碩士論文 972201035 詳細資訊




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姓名 曾宇揚( Yu-yang Tseng)  查詢紙本館藏   畢業系所 數學系
論文名稱 伽羅瓦理論
(Galois Theories)
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摘要(中) 在第二章,我重新整理了Lenstra的筆記和Grothendieck的SGA I的5.4章節。基本上可以分成兩個部分: 第一個部分根據Lenstra筆記的第三章。有一些比較省略的步驟,還有一些步驟留作習題,我把這些地方補上並想辦法寫得更流暢些。第二個部分根據Grothendieck的SGA I的5.4章節,用pro-objects的技術,首次出現是在Seminaire Bourbaki一篇Grothendieck的文章裡。我從原來文章裡簡短的描述中,給了定理4.1一個詳細的證明。
摘要(英) In chapter 2, I reorganize some part of cite{Le08} and cite{SGA1}. Basically it can be divided into two parts: the first part follows cite{Le08} Chapter 3. Some steps are written a bit roughly and some steps are exercises in original texts, I just make them more fluent, and write down the exercises; The second part follows cite{SGA1} Section 5.4, using the technique so called pro-objects, first introduced by Grothendieck in his article in Seminaire Bourbaki cite{Gr59}. I give a proof of cite{SGA1} Expos{e} V. Theorem 4.1, following the brief sketch in the original article.
關鍵字(中) ★ 伽羅瓦理論
★ 伽羅瓦範疇
★ 亞歷山大·格羅滕迪克
關鍵字(英) ★ Galois theory
★ Galois category
★ Grothendieck
論文目次 1 Preliminaries 3
1 Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Yoneda's Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Representable Functors . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Universal properties . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Limits and colimits . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Terminal and initial objects . . . . . . . . . . . . . . . . . . . . . 6
1.6 Inductive and Projective systems . . . . . . . . . . . . . . . . . . 6
1.7 Co nal functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.8 Filtered categories . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Group actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1 Initial topology and nal topology . . . . . . . . . . . . . . . . . 10
4 Pro nite groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.1 Projective system on topological spaces . . . . . . . . . . . . . . 12
4.2 Topological groups and continuous actions . . . . . . . . . . . . . 12
4.3 Pro nite groups . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.4 Continuous actions on topological spaces . . . . . . . . . . . . . . 14
II 17
2 Galois categories 19
1 Galois Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Bibliography . . . . . . . . . . 35
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指導教授 呂明光(Ming-guang Leu) 審核日期 2014-1-28
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