Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 114 / 1 / i / Solution

A one-term summand $\mathbb{Z}[i]$ becomes a one-term ${\mathbb{F}}_p$ complex after reduction modulo $p$. Its Bockstein homomorphism vanishes, so it contributes one $\mathbb{Z}/p$ summand to Bockstein homology in degree $i$.

Solved by gpt-5.6-sol high.