Algebraic K-theory of quasi-smooth blow-ups and cdh descent

We construct a semi-orthogonal decomposition on the category of perfect complexes on the blow-up of a derived Artin stack in a quasi-smooth centre. This gives a generalization of Thomason's blow-up formula in algebraic K-theory to derived stacks. We also provide a new criterion for descent in Voevodsky's cdh topology, which we use to give a direct proof of Cisinski's theorem that Weibel's homotopy invariant K-theory satisfies cdh descent.Comment: 24 pages; to appear in Annales Henri Lebesgu

The cdh-local motivic homotopy category

We construct a cdh-local motivic homotopy category SH_cdh(S) over an arbitrary base scheme S, and show that there is a canonical equivalence between SH_cdh(S) and SH(S). We learned this result from D.-C. Cisinski.Comment: 6 pages, posted on author's webpage in 2019; to appear in JPA

The derived homogeneous Fourier transform

We study a derived version of Laumon's homogeneous Fourier transform, which exchanges G_m-equivariant sheaves on a derived vector bundle and its dual. In this context, the Fourier transform exhibits a duality between derived and stacky phenomena. This is the first in a series of papers on derived microlocal sheaf theory.Comment: 29 page