# Atiyah–Bott formula

Short description: On the cohomology ring of the moduli stack of principal bundles

In algebraic geometry, the Atiyah–Bott formula says[1] the cohomology ring

$\displaystyle{ \operatorname{H}^*(\operatorname{Bun}_G(X), \mathbb{Q}_l) }$

of the moduli stack of principal bundles is a free graded-commutative algebra on certain homogeneous generators. The original work of Michael Atiyah and Raoul Bott concerned the integral cohomology ring of $\displaystyle{ \operatorname{Bun}_G(X) }$.