|
課程名稱 |
算術幾何專題
Topics in Arithmetic Geometry |
|
開課學期 |
102-1 |
|
授課對象 |
理學院 數學研究所 |
|
授課教師 |
余正道 |
|
課號 |
MATH5112 |
|
課程識別碼 |
221 U5530 |
|
班次 |
|
|
學分 |
3 |
|
全/半年 |
半年 |
|
必/選修 |
選修 |
|
上課時間 |
星期二1,2(8:10~10:00)星期五1,2(8:10~10:00) |
|
上課地點 |
天數102天數101 |
|
備註 |
上課時間:二9:00~10:15
五9:00~10:15
總人數上限：10人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1021ArithGeom |
|
課程簡介影片 |
|
|
核心能力關聯 |
本課程尚未建立核心能力關連 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
課程概述 |
Stationary phase principle, Witten’s proof of Morse inequality, Laumon’s proof of Weil conjecture, Fourier transform in other theories. |
|
課程目標 |
The theme of this course is the Fourier transform in arithmetic and algebraic geometry. We plan to start from the general idea of stationary phase principle in differential equations and then go through Witten’s approach to Morse theory. We then move to study the paper [L] where we use the theory of geometric Fourier transform to obtain some arithmetic results, including a product formula and a new proof of the Weil conjecture. We will review the necessary language of l-adic étale sheaves.
After the paper [L], the concepts of the local Fourier transform, the stationary phase principle and the product formula have been extended as useful tools to other theories in algebraic geometry, e.g. the D-module theory and p-adic cohomology theory. We plan to discuss some of these further developments too.
|
|
課程要求 |
Familiarity with algebra, algebraic topology |
|
預期每週課後學習時數 |
|
|
Office Hours |
另約時間 備註： By appointment |
|
指定閱讀 |
|
|
參考書目 |
[L] Laumon, Transformation de Fourier, constantes d’équations fonctionnelles et conjecture de Weil. 1987. |
|
評量方式
(僅供參考) |
|
|