Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations
What the paper claims, in its own words
For every sufficiently large admissible Hassett discriminant, a very general smooth complex cubic fourfold is irrational despite having both an untwisted geometric K3 category and an integral Hodge-theoretic K3 association. This disproves Kuznetsov's rationality conjecture and the sufficiency of the associated-K3 criterion for rationality; the discriminant threshold is ineffective.
The plain-language explainer for this entry is still coming.