Totaro's inequality for classifying spaces

Abstract

For a complex Lie group G and a prime number p, Totaro had conjectured that the dimension of the singular cohomology with Z/p-coefficients of classifying space of G is bounded above by that of the de Rham cohomology of the classifying stack of (the split form of) G in characteristic p. This conjecture was recently proven by Kubrak--Prikhodko. In this note, we give a shorter proof.

4 pages, comment welcome

References in corpus (2)

• Approximating classifying spaces by smooth projective varieties
• Computations of de Rham cohomology rings of classifying stacks at torsion primes