Vector bundles on algebraic varieties

  • Aravind Asok

    Department of Mathematics, University of Southern California, 3620 S. Vermont Ave., Los Angeles, CA 90089-2532, USA
  • Jean Fasel

    Institut Fourier, Universit Grenoble-Alpes, CS 40700, 38058 Grenoble cedex 9, France
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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.