課程資訊
課程名稱
動原與週期數
Motives and periods 
開課學期
109-2 
授課對象
理學院  數學系  
授課教師
余正道 
課號
MATH5264 
課程識別碼
221 U8910 
班次
 
學分
2.0 
全/半年
半年 
必/選修
選修 
上課時間
星期四3,4(10:20~12:10) 
上課地點
天數201 
備註
總人數上限:10人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1092motives 
課程簡介影片
 
核心能力關聯
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課程概述

Comparisons of cohomology theories, absolute Hodge cycles, Tannakian category, Nori’s construction, periods, exponential motives, special values as periods and their Galois groups 

課程目標
The theory of motives contains many central ideas in algebraic geometry. Although a large part of the structures of the theory remain conjectural, the philosophy has indeed provided useful guiding principles and served as the cores underlying different invariants by regarding them as various realizations of the common objects. The central topics of this course discuss the comparisons of different cohomology theories in algebraic geometry, regarded as various realizations of motives, the periods of motives and their structures. We focus on two constructions of motives: one uses the notion of absolute Hodge cycles and the other relies on Nori’s diagram categories. The Galois theory of the resulting periods will be discussed. Examples include the category generated by abelian varieties. Finally we move to the exponential motives recently developed by Fresan and Josse, which in particular provides a further factorizations of classical motives and potentially gives more links between differential Galois theory, Fourier transformation and transcendences of special values of interesting functions (e.g., Siegel’s E-functions). 
課程要求
Algebra, algebraic topology (including singular cohomology), working knowledges in algebraic geometry (including cohomology of coherent sheaves) 
預期每週課後學習時數
 
Office Hours
 
參考書目
Huber and Muller-Stach, Periods and Nori motives. Springer 2017.
Fresan and Josse, Exponential motives. 
指定閱讀
 
評量方式
(僅供參考)
   
課程進度
週次
日期
單元主題
無資料