Shafarevich counterexamples in dimension two and with large fundamental group
What the paper claims, in its own words
Constructs a smooth projective complex fourfold with large fundamental group whose universal cover contains no positive-dimensional compact analytic subvariety but is neither Stein nor holomorphically convex. A separate smooth projective complex surface already disproves unrestricted Shafarevich holomorphic convexity in dimension two.
The plain-language explainer for this entry is still coming.