Welcome to MathOverflow

Question

9

5

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

flag	asked Apr 19 2011 at 19:02 norondion 4,240●7●34

2

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 2011 at 19:11

Sean Tilson · Accepted Answer · 2011-04-20 14:53:25Z UTC

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.

Dan Ramras · Answer 2 · 2011-04-19 19:33:39Z UTC

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.

Chirag Lakhani · Answer 3 · 2011-04-19 23:56:59Z UTC

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/

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

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

3 Answers

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.