Abstract: Beilinson introduced an analogue of Kashiwara and Schapira's singular support for étale sheaves on a smooth scheme of equal characteristic. Recently, Saito has proposed an analogue of singular support for regular schemes in mixed characteristic, but it is only known to exist in some special examples. I will explain how to define a derived version of Verdier's specialization functor, and use it to give a candidate construction of the singular support in general.
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