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arXiv · 1712.06845

Conservative descent for semi-orthogonal decompositions

Daniel Bergh·Olaf M. Schnürer
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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.

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Daniel Bergh, Olaf M. Schnürer. 2019-12-19. Conservative descent for semi-orthogonal decompositions. https://doi.org/10.1016/j.aim.2019.106882

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