What question did this study set out to answer?

The aim is to establish the mod p cohomology ring formula for the classifying space BPU(p) when p is an odd prime.

February 12, 2026

A formula for the mod 𝑝 cohomology of 𝐵𝑃𝑈(𝑝)

Key Points

The aim is to establish the mod p cohomology ring formula for the classifying space BPU(p) when p is an odd prime.
Analyzed the mod p cohomology ring structure.
Developed parallels to Vistoli's formula for integral cohomology.
Provided a topological proof of Vistoli’s formula.
Proved a new mod p formula for the cohomology ring of BPU(p).
Demonstrated that the results parallel existing integral cohomology findings.
Offered a simpler topological proof for Vistoli’s formula.

Abstract

We study the mod p p cohomology ring of the classifying space B P U ( p ) BPU(p) of the projective unitary group P U ( p ) PU(p) , when p p is an odd prime. We prove a mod p p formula analogous to a formula of Vistoli for the integral cohomology ring of B P U ( p ) BPU(p) . As an application, we give a simple topological proof of Vistoli’s formula.

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A formula for the mod 𝑝 cohomology of 𝐵𝑃𝑈(𝑝)

Key Points

Abstract

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