Suppose you grasped and enjoyed reading Quillen's "Higher Algebraic K-theory I". Now, if you could go back in time to when you started studying algebraic topology and create a reading list / roadmap with the above paper as a goal, what would this plan look like?
Here's another version of the question: suppose you're the PhD advisor of a student that's recently finished their undergrad degree and in terms of books background has only read and completed most of the exercises in:
- algebraic geometry: all of Q. Liu's book
- algebraic topology: first two chapters of W. Massey's intro book
- differential geometry: first half of J. Lee's smooth manifolds book
Which books and papers (and in what order) should this student master in order to understand (or at least appreciate) most of Quillen 1?
The above questions are likely quite vague wrt to "how do I learn modern algebraic k theory?", but hopefully they're somewhat concrete by stating i) the goal [Quillen 1] and ii) the starting maths background.
If it helps, assume a secondary goal is to eventually focus on studying/appreciating arithmetic problems like Parshin's conjecture.