Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $k$ be a field (of char. not $2$) and $X_k=\text{Spec} (k[x_1,\cdots,x_n]/(x_1^2+\cdots +x_n^2-1))$. Do we know the Chow groups $A_i (X_k)$? I could not find any references, even for $X_{\mathbb R}$.

What (I think) I know: the K-groups were computed by Swan, so we know the total Chow group up to torsions. In codimension $1$ (i.e., class groups) I am fairly certain the answers are known.

share|improve this question
add comment

1 Answer 1

up vote 4 down vote accepted

The book

The Algebraic and Geometric Theory of Quadratic Forms. by R. Elman, N. Karpenko and A. Merkurjev (American Mathematical Society Colloquium Publications, 56., American Mathematical Society, Providence, RI, 2008. 435 pp.)

contains a lot of information. I was just reading

B. Totaro, The automorphism group of an affine quadric, Math. Proc. Cambridge Philos. Soc. (2007) vol. 143 (1) pp. 1-8

and he is referring to this book for information on Chow groups of spheres.

share|improve this answer
Thank you Andreas, this looks promising. I will try to look at it carefully when I have some time. –  Hailong Dao Oct 26 '10 at 2:11
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.