Atiyah–Bott formula

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

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

of the moduli stack of principal bundles is a free graded-commutative algebra on certain homogeneous generators. Atiyah and Bott's original work concerned integral cohomology ring of Bun_G(X).

See also

• Borel's theorem, which says the cohomology ring of a classifying stack is a polynomial ring.

Notes

1. Gaitsgory–Lurie, § 6.2.

References

• Atiyah, M. F. and R. Bott.; "The Yang-Mills equations over Riemann surfaces." Philos. Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505.
• Gaitsgory, D; Lurie, J.; "Weil's Conjecture for Function Fields." 2014,