
## 11. Moduli Stack of Torsion Coherent Sheaves on $\mathbb{P}^1$

1. #### Problem 11.1.

[McNamara] Let $X$ be the moduli stack of torsion coherent sheaves on $\mathbb{P}^1$ over $\C$. Is it true that $H^{\mathrm{odd}}(X, k) = 0$ for all fields $k$?

(Motivated by KLR algebras for affine $\mathfrak{sl}_2$.)

Cite this as: AimPL: Sheaves and modular representations of reductive groups, available at http://aimpl.org/sheavemodular.