A primer for unstable motivic homotopy theory

Abstract

In this expository article, we give the foundations, basic facts, and first examples of unstable motivic homotopy theory with a view towards the approach of Asok-Fasel to the classification of vector bundles on smooth complex affine varieties. Our focus is on making these techniques more accessible to algebraic geometers.

Many updates and corrections, 58 pages, to appear in the proceedings volume "Bootcamp for the 2015 Algebraic Geometry Summer Research Institute (Utah, 2015)"

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