Spring 2026 Topics in Algebraic Geometry: Algebraic Cycles

Content

We first study basic concepts in algebraic cycles: rational equivalence, Chow groups, Chern and Segre classes, Gysin maps, intersection products, Grothendieck-Riemann-Roch, and motives. We then define and study higher Chow groups and motivic cohomology.

General Information

Instructor Fumiaki Suzuki

Email Address suzuki [at] bicmr.pku.edu.cn

Class Time Tuesdays 1-2, and Thursdays 5-6 in odd weeks

Class Location 三教308

References Fulton, W.: "Intersection Theory"
Bloch, S.: "Algebraic cycles and higher K-theory"
Bloch, S.: "The moving lemma for higher Chow groups"
Mazza, C., Voevodsky, V., Weibel, C.: "Lecture notes on motivic cohomology"
Levine, M.: "Mixed Motives"

Grading Policy TBA

Tentative Schedule

We cover Chapters 1, 2, 3, 4, 5, 6, 7, 8, 15, 16 of Fulton in the first 10 weeks, and spend the rest of the semester on Bloch's papers and Chapters 1, 2, 3, 17, 18, 19 of Mazza-Voevodsky-Weibel.

Instructor	Fumiaki Suzuki
Email Address	suzuki [at] bicmr.pku.edu.cn
Class Time	Tuesdays 1-2, and Thursdays 5-6 in odd weeks
Class Location	三教308
References	Fulton, W.: "Intersection Theory" Bloch, S.: "Algebraic cycles and higher K-theory" Bloch, S.: "The moving lemma for higher Chow groups" Mazza, C., Voevodsky, V., Weibel, C.: "Lecture notes on motivic cohomology" Levine, M.: "Mixed Motives"
Grading Policy	TBA