課程名稱 |
代數幾何 Algebraic Geometry |
開課學期 |
112-2 |
授課對象 |
理學院 數學研究所 |
授課教師 |
莊武諺 |
課號 |
MATH5146 |
課程識別碼 |
221 U3600 |
班次 |
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學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期二8,9(15:30~17:20)星期四8,9(15:30~17:20) |
上課地點 |
天數201天數201 |
備註 |
總人數上限:30人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
sheaf theory, schemes, separated and proper morphisms, sheaves of modules, divisors, projective morphisms, differentials, formal schemes.
derived functors, cohomology of sheaves, cohomology of a Noetherian affine scheme, Cech cohomology, cohomology of projective spaces, Ext groups, Serre duality, higher direct images, flat morphisms, smooth morphisms, formal functions, semicontinuity theorem. |
課程目標 |
待補 |
課程要求 |
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預期每週課後學習時數 |
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Office Hours |
每週一 12:00~13:30 |
指定閱讀 |
Hartshorne, Algebraic Geometry.
Vakil, THE RISING SEA: Foundations of Algebraic Geometry, available online. http://math.stanford.edu/~vakil/216blog/ |
參考書目 |
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評量方式 (僅供參考) |
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週次 |
日期 |
單元主題 |
第1週 |
2/20, 2/22 |
sheaf theory, schemes. |
第2週 |
2/27, 2/29 |
Spec, schemes, Proj construction. |
第3週 |
3/5, 3/7 |
fiber products of schemes, separated morphism. |
第4週 |
3/12, 3/14 |
separated and proper morphisms, sheaves of modules. |
第5週 |
3/19, 3/21 |
sheaves of modules. |
第6週 |
3/26, 3/28 |
divisors. |
第7週 |
4/2 |
projective morphisms, relative Proj. |
第8週 |
4/9, 4/11 |
blowing-ups, differentials. |
第9週 |
4/16, 4/18 |
differentials, derived functors, cohomology of sheaves. |
第10週 |
4/23, 4/25 |
cohomology of a Noetherian affine scheme, Cech cohomology. |
第11週 |
4/30, 5/2 |
cohomology of projective spaces, Ext groups and sheaves. |
第12週 |
5/7, 5/9 |
Serre duality, higher direct images of sheaves. |
第13週 |
5/14, 5/16 |
flat morphisms. |
第14週 |
5/21, 5/23 |
smooth morphisms. |
第15週 |
5/28, 5/30 |
formal schemes, formal functions. |
第16週 |
6/4, 6/6 |
semicontinuity theorem. |
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