evals/fixtures/modular-rank.md

# Claim and proposed proof

Let C be the cochain complex of free abelian groups with C^0 = Z, C^1 = Z,
zero in other degrees, and differential d^0(x) = 2x. Let D be the zero complex.

Claim: Since C tensor Q and D tensor Q have the same cohomology, C tensor F_p
and D tensor F_p have the same cohomology for every prime p.

Proposed proof: The differential matrix of C has full rank over Q, so it has
full rank after reduction modulo every prime. Consequently both complexes have
zero cohomology in every degree after reduction.