Appears in collection : Algèbre, Géométrie et Physique : une conférence en l'honneur

For a morphsm of schemes $f:X\rightarrow Y$ of finite Tor-dimension we will define certain "relative derived categories", which are intermideate triangulated categories between the perfect derived category and derived category of coherent sheaves on X. They are closely related with categories of matrix factorizations on a singular scheme. We will discuss the Thomason localization theorem for these categories. In particular we will see that localization fails for the naive version of the category of "perfect" matrix factorizations.