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課程名稱 |
代數數論中的p進方法和岩澤理論
Introduction to Iwasawa theory |
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開課學期 |
109-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
謝銘倫 |
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課號 |
MATH5257 |
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課程識別碼 |
221 U8960 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期五6,7,8(13:20~16:20) |
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上課地點 |
天數201 |
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備註 |
總人數上限：20人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1092MATH5257_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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課程概述 |
The tentative course syllabus:
1. Bernoulli numbers, Dirichlet L-values and Kummer congruences.
2. Gauss sums and Stickelberger-Herbrand's theorem.
3. Cyclotomic units and Ribet's theorem (I) : Preliminaries.
4. Cyclotomic units and Ribet's theorem (II): Euler system argument.
5. Kubota-Leopodlt p-adic L-functions.
6. Iwasawa modules associated with ideal class groups.
7. Local units and Coates-Wiles homomorphism.
8. Kolyvagin-Rubin's proof of Iwasawa main conjecture over Q.
9. Sinnot's proof of the vanishing of mu-invariant. |
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課程目標 |
The goal of this course is to provide an introduction to classical Iwasawa theory and the proof of Iwasawa main conjecture via the Euler system for cyclotomic units. |
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課程要求 |
Standard knowledge on p-adic numbers and Dirichlet L-functions: Chaper I-VI in "A course in arithmetic" by J.-P. Serre.
Basic algebraic number theory: Algebraic number theory: proceedings edited by Cassels and Frohlich, Chapter I-VII. At least Chapter 1-4 and Chapter 8 in "Number fields" by D. Marcus. |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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參考書目 |
Introduction to cyclotomic fields (GTM 83), by L. Washington.
The paper "Iwasawa theory for elliptic curves" by R. Greenberg in Lecture notes of mathematics 1716 |
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評量方式
(僅供參考) |
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