A note on specializing semi-orthogonal decompositions
Weimufei Wu
TL;DR
This paper demonstrates that families of semi-orthogonal decompositions fail to meet the valuative criterion for properness, providing a negative answer to a previously posed question.
Contribution
It establishes a negative result regarding the properness of families of semi-orthogonal decompositions, addressing an open question in the field.
Findings
Families of semi-orthogonal decompositions do not satisfy the existence part of the valuative criterion for properness.
Provides a counterexample or proof of non-existence in the context of semi-orthogonal decompositions.
Answers a question posed by Belmans, Okawa, and Ricolfi with a negative result.
Abstract
We prove that families of semi-orthogonal decompositions do not satisfy the existence part of the valuative criterion for properness, giving a negative answer to a question posed by Belmans, Okawa, and Ricolfi.
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Taxonomy
TopicsAdvanced Algebra and Logic · Matrix Theory and Algorithms · Advanced Numerical Analysis Techniques