代数几何讨论班

报告人：徐泽 (山东大学 154.com皇冠)

报告时间:  2022年10月20日，10月27日，11月03日

(周四)上午10：00-11:00

腾讯会议号：998-8596-4804 密码: 2022

报告题目: An introduction to the theory of Chow motives

报告摘要:

The theory of motives, which is envisioned by Grothendieck as a “universal” cohomology theory for algebraic varieties in the mid-sixties, lies in the heart part of the theory of algebraic cycles. Several important conjectures on algebraic cycles are closely related to motives. In this series of lectures, we introduce fundamentals of pure motives and Chow groups, which at least include adequate equivalence relations on algebraic cycles, construction of Chow motives, Manin’s identity principle, Jannsen’s theorem, finite-dimensionality of Chow motives, Chow-Künneth decomposition for varieties, related conjectures on algebraic cycles and so on.

Lecture 1. We start with a short outline of algebraic cycles and Chow groups, which are at the basis of the entire theory. Then we describe Grothendieck’s construction of the category of pure motives and some examples, in particular motives of curves.

Lecture 2. We discuss the standard conjectures and Jannsen’s theorem which shows that the category of pure motives modulo numerical equivalence is an abelian semi-simple category. Then we introduce the remarkable concept of “finite-dimensionality” for pure motives in the sense of Kimura-O’Sullivan and the surprising properties.

Lecture 3. We talk about the Bloch-Beilinson conjecture on Chow groups and Murre’s reformulation based on Chow-Künneth decomposition for varieties. Then, we focus on the case of surfaces. If time permits, we discuss motivic multiplicativity.

报告人简介:

徐泽, 中国科学院数学与系统科学研究院基础数学专业博士毕业，现任山东大学数学学院副教授。研究方向是代数几何，研究领域为代数链(Algebraic Cycle)理论，已在Int. Math. Res. Not., Comm. Algebra, J. K-Theory等著名期刊发表论文。