# learning $\mathbf{A}^1$-homotopy theory

If you wanted to learn $\mathbf{A}^1$-homotopy theory, which sources in which order would you use?

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It of course depends on what you know. If you don't have substantial experience with model categories and simplicial sets, they are prerequisites to $\mathbf{A}^1$ homotopy theory. – Harry Gindi Apr 19 '11 at 19:11

A book that might be helpful, that is probably mentioned on website above is http://www.amazon.com/Motivic-Homotopy-Theory-Nordfjordeid-Universitext/dp/3540458956/ref=sr_1_1?ie=UTF8&qid=1303257360&sr=8-1

Also, people now call it Motivic instead of $\mathbb{A}^1$ sometimes.

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Dan Dugger's paper on the subject is an extremely valuable reference, since he manages to set up the foundations in a natural manner. Some familiarity with model categories is certainly needed. A version is available on his web page:

http://pages.uoregon.edu/ddugger/univ.html

Of course the long Morel-Voevodsky paper is the original reference. It has a lot of good information, although I did not find it easy going.

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Aravind Asok has an entire website devoted to pointing out resources for learning $\mathbf{A}^1$-homotopy theory. It is organized quite well. The concept list section of the page has lots of wikipedia-like entries on topics related to $\mathbf{A}^1$-homotopy theory.

http://a1homotopy.tiddlyspot.com/

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