Stratification for module categories of finite group schemes Dave Benson, Srikanth B. Iyengar, Henning Krause, and Julia Pevtsova \begin{abstract} The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning the structure of the stable module category and the behavior of support and cosupport under restriction and induction are presented. \end{abstract} \keywords{cosupport, finite group scheme, localising subcategory, support, thick subcategory} \subjclass[2010]{16G10 (primary); 20G10, 20J06 (secondary)}