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 L\"uroth problem
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abstract
Notes of my lectures at the CIME (Levico Terme, june 2015). The lectures gave an overview of the L\"uroth problem, its history, the counter-examples found in the 70's, and the recent developments on stable rationality following the new method introduced by C. Voisin.
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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.