An atomic approach to Shokurov's conic-bundle conjecture

In this paper, we apply a weaker version of Hodge atoms to show that a standard conic bundle over a smooth complex projective rational surface $S$ is irrational if $|2K_S+Δ|\ne\emptyset$, where $Δ$ is the discriminant divisor. This proves Shokurov's conjecture on rationality of conic bundle threefolds. As an application, we deduce precisely which nodal quartic double solids are rational.