Orlov's perfect-dg-category phantom conjecture
Orlov's perfect-dg-category phantom conjecture
A phantom is a nonzero admissible subcategory whose Grothendieck group vanishes. Let be a smooth finite-dimensional dg-algebra, and let denote the dg-category of perfect dg-modules over . Orlov's conjecture. There are no phantoms of the form
The phantom arising from the non-full maximal-length exceptional collection on the ten-point blow-up of disproves this conjecture.
Sources & referencesView supporting material
Primary source
Johannes Krah, “A Phantom on a Rational Surface”, arXiv:2304.01269 (2023).
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