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2 votes
1 answer
400 views

${\rm SL}_2(\mathbb C)$-equivariant K-theory of $\mathbb C P^1$

Consider the action of ${\rm SL}_2(\mathbb C)$ on $\mathbb C P^1$ induced by the action of 2×2 matrices on 2-vectors. Is it true that $K^{{\rm SL}_2(\mathbb C)}(\mathbb C P^1)$ is $\mathbb C[t,t^{-1}]$...
Yellow Pig's user avatar
  • 2,964
0 votes
1 answer
204 views

Equivariant sheaves on $\mathbb P^1$

Let $K(\mathbb P^1)$ be the Grothendieck group of sheaves on $\mathbb P^1$. I want to show that the map $K^{{\rm PGL}(2)\times \{\pm 1\}}(\mathbb P^1) \to K(\mathbb P^1)$ is not onto. I read somewhere ...
Yellow Pig's user avatar
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25 votes
1 answer
839 views

Vector bundles on $\mathbb{A}^n / G$

Let $G$ be a finite group acting linearly on $\mathbb{A}^n$. Do we expect algebraic vector bundles on $X := \mathbb{A}^n/G$ to be trivial? Here by the quotient I mean the singular scheme, not the ...
Evgeny Shinder's user avatar