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February 12, 2026Proceedings of the American Mathematical Society0 citations

A formula for the mod 𝑝 cohomology of π΅π‘ƒπ‘ˆ(𝑝)

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JZJiaxi Zha

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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Cite This Study

Jiaxi Zha (2026) studied this question.

synapsesocial.com/papers/698d6d795be6419ac0d5267dhttps://doi.org/10.1090/proc/17569
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