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

Let $G$ be a connected linear algebraic group over $\mathbb{C}$ and $X$ a $G$-variety. Let $K_G^0(X)$ be the Grothedieck group of coherent $G$-equivariant sheaves on $X$, and $K_G^i(X)$ for $i>0$ the higher analogues of $K_G^0(X)$ (Quillen, Thomason). My question is that when $X=\text{pt}$ is a single point, do we have $K_G^i(\text{pt})=0$ for $i>0$?

share|improve this question

1 Answer 1

If your point is $Spec({\mathbb C})$ and $G$ is the trivial group, then $K^i_G(pt)$ contains a rational vector space of uncountable dimension for every $i>0$.

share|improve this answer

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.