Codimension 1 foliations with numerically trivial canonical class on singular spaces

International audienceIn this article, we describe the structure of codimension one foliations with canonical singularities and numerically trivial canonical class on varieties with terminal singularities, extending a result of Loray, Pereira and Touzet to this context. Contents 1. Introduction 1 2. Notation, conventions, and used facts 4 3. Foliations 7 4. Singularities of foliations 10 5. Weakly regular foliations on singular spaces 17 6. Weakly regular foliations with algebraic leaves 25 7. Quasi-étale trivializable reflexive sheaves 28 8. A global Reeb stability theorem 30 9. Algebraic integrability, I 36 10. Algebraic integrability, II 40 11. Foliations defined by closed rational 1-forms 44 12. Proofs of Theorems 1.1 and 1.3 and proof of Corollary 1.4 51 References 5