I've often heard that one of the benefits of derived algebraic geometry, next to a cleaner intersection theory, is that "provides natural settings " for the $\mathbb{A}^1$-homotopy theory (the quote comes from Wikipedia's article on Derived Algebraic Geometry https://en.wikipedia.org/wiki/Derived_algebraic_geometry). However, I have not found an introduction to this online. Could someone explain how derived schemes show up in $\mathbb{A}^1$-homotopy theory and/or point me to a nice introduction to this?
Asked
Active
Viewed 155 times
4
-
6The only source I know of which explains explicitly how to interpret derived geometry within motivic homotopy theory is the work of Adeel Khan quoted in the wikipedia article. This is not old enough to be part of a text book. – D.-C. Cisinski Aug 04 '20 at 20:09