We define inertial blocks of finite groups over arbitrary fields and prove that a block covered by an inertial block over a bigger field of characteristic p is still inertial if p is odd or if the inertial block has abelian defect groups. Combined with some known facts, this result implies that Broué's conjecture over arbitrary fields holds for many blocks, for example, blocks for p-solvable groups with abelian defect groups. Consequently, we partially prove Puig's finiteness conjecture for inertial blocks over f...
