AbstractLet X be an algebraic variety over a base scheme S and ?:T→S a base change. Given an admissible subcategory ???? in ????b(X), the bounded derived category of coherent sheaves on X, we construct under some technical conditions an admissible subcategory ????T in ????b(X×ST), called the base change of ????, in such a way that the following base change theorem holds: if a semiorthogonal decomposition of ????b (X) is given, then the base changes of its components form a semiorthogonal decomposition of ????b (X×ST) . As an intermediate step, we construct a compatible system of semiorthogonal decompositions of the unbounded derived category of quasicoherent sheaves on X and of the category of perfect complexes on X. As an application, we prove that the projection functors of a semiorthogonal decomposition are kernel functors.
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