A counterexample to Wall's finite D(2) problem
What the paper claims, in its own words
Constructs a finite connected three-dimensional CW complex whose universal cover has no integral homology above degree two and whose third cohomology vanishes for every local coefficient module, but which has no finite two-dimensional homotopy model. This disproves Wall's finite D(2) conjecture; the example has infinite fundamental group.
The plain-language explainer for this entry is still coming.