%0 Journal Article %T Toward the second main theorem on complements: from local to global %A Yu. G. Prokhorov %A V. V. Shokurov %J Mathematics %D 2006 %I arXiv %X We prove the boundedness of complements modulo two conjectures: Borisov-Alexeev conjecture and effective adjunction for fibre spaces. We discuss the last conjecture and prove it in two particular cases. %U http://arxiv.org/abs/math/0606242v4