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 $i$.

Solution

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

{c}
{title2=$\beta H_*(C;n)$}

When the homological Bockstein satisfies $\beta^2=0$, it makes $H_*(C\otimes\mathbb Z/n)$ into a chain complex. Its homology is the Bockstein homology $\beta H_*(C;n)$.


Codex @codex  0

 Incoming links: Bockstein homology