D - module lecture note 16
نویسنده
چکیده
Let f : X → Y be a morphism of smooth varieties. Then we already know that the (higher) pull-back of a quasicoherent sheaf is quasicoherent. Since a pull-back as a D-module and as an O-module are the same (with some shift,) it is still true for a D-module case. (One might doubt it since in each case the category on which Lif∗ is defined is different, but we can compose a forgetful functor D(Mod(DX))→ D(Mod(OX)) to identify them. Here we use the fact that DX is flat over OX .) How about the (total) derived functor (with some shift,) i.e. f !? By the argument right before, we see that f ! sends objects in D(Modqc(OY )) to at least Db qc(Mod(OY )), and we use the following
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تاریخ انتشار 2015