报告人: 储诚浩

时间: 2013年1月4、5、7、8、9、10日的10：00-11：00, 其中1月8日为8:30-9:30.

地点: 致远楼108

摘要: In these lectures we plan to discuss the history, important results and current development of the theory of motives. We plan to proceed according to the following schedule.

Lecture 1( 1月4日) Overview of motive.

Weil Conjecture. Grothendieck's idea. Beilinson Conjecture and Voevodsky's triangulated category of motives. Motives over fields of finite characters. Grothendieck's standard conjectures. Motivic t-structure. Absolute motives or motives over F1. Riemann Hypothesis.

Lecture 2( 1月5日) Topological backgrounds.

Homotopy category of topological spaces. Artiyah-Hirzebruch spectral sequences. Simplical methods. Dold-Thom theorem.

Lecture 3( 1月7日) Homological backgrounds.

Spectral sequences from bicomplexes and filtrations. Intersection numbers. Grothendieck topologies. Sites.

Lecture 4( 1月8日) Voevodsky's triangulated category of motives I

Construction and basic properties.

Lecture 5( 1月9日) Voevodsky's triangulated category of motives II

Applications: spectral sequence relating K-theory. Bloch's higher Chow group. Milnor K-group. Vanishing Conjecture and Motivic t-structure. Bloch-Kato conjecture.

Lecture 6( 1月10日) Lawson homology and Grothendieck's standard conjectures.

Beilinson's 2010 paper and Suslin Conjecture.