125 research outputs found
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
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