Classifying Spaces of Algebraic Groups

Nikita Karpenko (University of Alberta)

Jan 1, 2023 — Apr 30, 2022

About the course

Classifying spaces of algebraic groups do not exist in classical algebraic geometry. However, they can be approximated by algebraic varieties. Using this approach, Burt Totaro defined the Chow ring CH(BG) of algebraic cycles on the classifying space BG of an affine algebraic group G. The representation ring R(G) can be viewed as the Grothendieck ring of BG. It turns out that the rings CH(BG) and R(G) are related the same way as the Chow ring and the Grothendieck ring of a smooth algebraic variety are. Namely, for elements of R(G) one can define their Chern classes with values in CH(BG). And there is a surjective ring homomorphism of CH(BG) onto the graded ring associated with certain filtration on R(G). We discuss these and related objects, consider examples of their computation, review some applications. We also take a look at the rationality problem of BG. We start with a quick introduction into algebraic groups and into the theory of Chow rings of algebraic varieties.


This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

Enrollment Details

Course Name
Classifying Spaces of Algebraic Groups
Jan 1, 2023 — Apr 30, 2022
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For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

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