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.
The Derived Category of the Intersection of Four Quadrics
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abstract
The derived category of a general complete intersection of four quadrics in P^{2n-1} has a semi-orthogonal decomposition < O(-2n+9), ..., O(-1), O, D >, where D is the derived category of twisted sheaves on a certain non-algebraic complex 3-fold coming from a moduli problem. In particular, when n=4 we obtain a (twisted) derived equivalence of Calabi-Yau 3-folds predicted by Gross. This differs from Kuznetsov's result in that our construction is geometric and avoids non-commutative varieties.
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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.