319 research outputs found
Conservative descent for semi-orthogonal decompositions
Motivated by the local flavor of several well-known semi-orthogonal
decompositions in algebraic geometry, we introduce a technique called
conservative descent, which shows that it is enough to establish these
decompositions locally. The decompositions we have in mind are those for
projectivized vector bundles and blow-ups, due to Orlov, and root stacks, due
to Ishii and Ueda. Our technique simplifies the proofs of these decompositions
and establishes them in greater generality for arbitrary algebraic stacks.Comment: Final versio
New enhancements of derived categories of coherent sheaves and applications
We introduce new enhancements for the bounded derived category
of coherent sheaves on a suitable scheme and for its subcategory
of perfect complexes. They are used for translating Fourier-Mukai functors to
functors between derived categories of dg algebras, for relating homological
smoothness of to geometric smoothness of and for proving
homological smoothness of Moreover, we characterize properness
of and geometrically.Comment: 61 pages, minor change
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