Authors define Lichtenbaum-Quillen dimension of complex varieties from K-theory stabilization and apply it to rationality obstructions and new cases of the integral Hodge conjecture.
Geometric Phantom Categories
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abstract
In this paper we give a construction of phantom categories, i.e. admissible triangulated subcategories in bounded derived categories of coherent sheaves on smooth projective varieties that have trivial Hochschild homology and trivial Grothendieck group. We also prove that these phantom categories are phantoms in a stronger sense, namely, they have trivial K-motives and, hence, all their higher K-groups are trivial too.
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2023 1verdicts
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The Lichtenbaum-Quillen dimension of complex varieties
Authors define Lichtenbaum-Quillen dimension of complex varieties from K-theory stabilization and apply it to rationality obstructions and new cases of the integral Hodge conjecture.