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課程名稱 |
動原與週期數
Motives and periods |
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開課學期 |
109-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
余正道 |
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課號 |
MATH5264 |
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課程識別碼 |
221 U8910 |
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班次 |
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學分 |
2.0 |
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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 |
星期四3,4(10:20~12:10) |
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上課地點 |
天數201 |
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備註 |
總人數上限：10人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1092motives |
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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 |
Comparisons of cohomology theories, absolute Hodge cycles, Tannakian category, Nori’s construction, periods, exponential motives, special values as periods and their Galois groups |
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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). |
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課程要求 |
Algebra, algebraic topology (including singular cohomology), working knowledges in algebraic geometry (including cohomology of coherent sheaves) |
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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 |
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參考書目 |
Huber and Muller-Stach, Periods and Nori motives. Springer 2017.
Fresan and Josse, Exponential motives. |
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評量方式
(僅供參考) |
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