代数学特論D

【講義の概要とねらい】
　Motivated by Weil's beautiful conjectures on zeta functions counting points on varieties over finite fields, étale cohomology is a theory generalising singular cohomology of complex algebraic varieties. In the first half we give an introduction to the classical theory of étale cohomology. In the second half, we will discuss Bhatt-Scholze's pro-étale topology. For more information see: http://www.math.titech.ac.jp/~shanekelly/EtaleCohomology2018-19WS.html

【到達目標】
(1) Obtain overall knowledge on basics in étale cohomology
(2) Understand the relationship between étale topology and Galois theory
(3) Attain understanding of possible applications of étale topology

【キーワード】
Étale cohomology, homological algebra, Galois theory

【学生が身につける力】
専門力

【授業の進め方】
Standard lecture course

【授業計画・課題】

第1回	The pro-étale topology
第2回	Commutative algebra II
第3回	Homological algebra II
第4回	Topology II
第5回	Functoriality II
第6回	Functoriality III
第7回	Functoriality IV
第8回	Fundamental group II

課題は講義中に指示する

【教科書】
None required

【参考書、講義資料等】
Milne, James S. "Etale cohomology, volume 33 of Princeton Mathematical Series." (1980).
Bhatt, Bhargav, and Peter Scholze. "The pro-\'etale topology for schemes." arXiv preprint arXiv:1309.1198 (2013).

【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.A403 ：代数学特論C
MTH.A301 ：代数学第一
MTH.A302 ：代数学第二

【履修の条件（知識・技能・履修科目等）】
Basic knowledge of scheme theory (e.g., Hartshorne)