Conservative descent for semi-orthogonal decompositions

Abstract

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.

Final version

References in corpus (1)

• Semiorthogonal decompositions in algebraic geometry

Cited by in corpus (4)

• K-theory and the singularity category of quotient singularities
• Derived categories of Quot schemes of locally free quotients
• Gluing semi-orthogonal decompositions
• A power structure over the Grothendieck ring of geometric dg categories