As I'm currently reading Morel&Voevodskys paper on A¹-homotopy theory of schemes, I will by and by write a little "walk-through" with hints & comments on how to find additional information to better (or even start to) understand the paper. Maybe for a newcomer to the subject (like me) it's difficult at first to stick together all these concepts like model theory, simplicial objects, Grothendieck topologies, algebraic geometry and so on. I will try to provide helpful comments to make the paper more accessible to those who are not that familiar with these notions above.

Continue reading «Walk-through to Morel-Voevodsky: A¹-homotopy theory of schemes (1999)»

I just found this very nice talk of Voevodsky (2002) about $A^1$-Homotopy Theory - where he explains it for non-mathematicians :-)

The PDF is available here, the video is available at Clay Mathematics Institute: Voevodskys talk about A1-Homotopy Theory

Maybe your browser can show embedded videos (via HTML5 video tag):

Further reading:

• Introductory paper, written for mathematicians who know only basic standard homotopy theory
• What do you have to read first?
• The main paper by Voevodsky & Morel