Vector bundles on algebraic varieties
Aravind Asok
Department of Mathematics, University of Southern California, 3620 S. Vermont Ave., Los Angeles, CA 90089-2532, USAJean Fasel
Institut Fourier, Universit Grenoble-Alpes, CS 40700, 38058 Grenoble cedex 9, France
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Abstract
We survey recent developments related to the problem of classifying vector bundles on algebraic varieties. We focus on the striking analogies between topology and algebraic geometry, and the way in which the Morel–Voevodsky motivic homotopy category can be used to exploit those analogies.