Aravind Asok, Jean Fasel
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.
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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.
Key concepts: Vector bundle, Mathematics, Pure mathematics, Vector (molecular biology), Algebraic number, Algebra over a field, Biology, Mathematical analysis