Dévissage for periodic cyclic homology of complete intersections (Q6590094)

Let \(X\) be a smooth schme and \(Z\subseteq X\) a locally complete intersection closed embedding. The main result states that such an embedding induces a quasi-isomorphism betweeen the periodic cyclic complexes of the dg derived category of \(Z\) and the dg derived category of sheaves on \(X\) supported on \(Z\). This theorem is viewed as a devissage property for periodic cyclic homology.\N\NThere are two applications. The first one is about new cases of Blanc's lattice conjecture for the dg derived category and the dg singularity category (Theorem 1.4). The second one is about an expliction computation of the boundary map in n a certain localization sequence on periodic cyclic homology (Theorem 5.5).