### 2018年度　代数学特論H   Advanced topics in Algebra H

KELLY SHANE ANDREW

メディア利用

クラス
-

MTH.A504

1

2018年度

4Q
シラバス更新日
2018年9月17日

-

アクセスランキング
media

### 講義の概要とねらい

Algebraic cycles are a central theme in algebraic geometry, appearing in places such as Abel’s Theorem, The Riemann-Roch Theorem, enumerative geometry, higher K-theory, motivic cohomology, and the Hodge conjecture. In this course we develop some basic ideas, and review some of these applications. For more information see: http://www.math.titech.ac.jp/~shanekelly/Cycles2018-19WS.html

### 到達目標

(1) Obtain overall knowledge on basics of algebraic cycle theories, such as Chow groups
(2) Understand the relationship between Chow groups and other theories, such as de Rham cohomology
(3) Attain basic understanding of motivic cohomology

### キーワード

Algebraic cycles, Chow groups, motivic cohomology

### 学生が身につける力(ディグリー・ポリシー)

 ✔ 専門力 教養力 コミュニケーション力 展開力(探究力又は設定力) 展開力(実践力又は解決力)

### 授業の進め方

Standard lecture course

授業計画 課題

None required

### 参考書、講義資料等

Murre, Lectures on algebraic cycles and Chow groups
Mazza, Carlo, Vladimir Voevodsky, and Charles A. Weibel. Lecture notes on motivic cohomology. Vol. 2. American Mathematical Soc., 2011.

### 成績評価の基準及び方法

Course scores are evaluated by homework assignments. Details will be announced during the course.

### 関連する科目

• MTH.A301 ： 代数学第一
• MTH.A302 ： 代数学第二
• MTH.A331 ： 代数学続論
• MTH.A503 ： 代数学特論G

### 履修の条件(知識・技能・履修済科目等)

Basic knowledge of scheme theory (e.g., Hartshorne)