mathematics and other sciences, useful software and some philosophy
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A¹ denotes the affine line, which is Spec k[x] when working over a field.
Is it possible to prove the Quillen-Suslin theorem analogous to the classical theorem on vector bundles over contractible spaces via representing the vectorbundle-up-to-iso-functor in the homotopy category by infinite Grassmannians?
This is an extended abstract for Konrad Voelkel's diploma thesis.
Chapter 2.1. Homotopy theory of simplicial sheaves: The simplicial model category structure. Discussion of 1.2, 1.3, 1.4, 1.5, 1.6, 1.8, 1.9, 1.10.
Background needed to understand Morel-Voevodsky's paper "A¹-homotopy theory". I explain simplicial sets, topoi, monoidal categories, enriched categories and simplicial model categories.
content on Konrad Voelkel's Blog – Mathemagically is licensed under CC-BY-NC 3.0, if not indicated otherwise.
http://blog.konradvoelkel.de/2012/01/serres-problem-via-motivic-homotopy/
