If you wanted to learn $\mathbf{A}^1$-homotopy theory, which sources in which order would you use?
$\begingroup$
$\endgroup$
1
-
2$\begingroup$ 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. $\endgroup$– Harry GindiCommented Apr 19, 2011 at 19:11
Add a comment
|
3 Answers
$\begingroup$
$\endgroup$
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.
answered Apr 19, 2011 at 23:57
$\begingroup$
$\endgroup$
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.
answered Apr 19, 2011 at 19:33
$\begingroup$
$\endgroup$
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.
