First of the questions about derived algebraic geometry from a noobie.

The way I understand it, every discrete ring R corresponds to some \infty-spectrum ring spectrum whose \pi_0 is R. Now consider p-adic numbers. They are a limit of discrete rings — what should correspond to them? How to generalize?

(+ what could be good tags for derived algebraic geometry? I was considering: e-infinity, infty-structures, math-0703204, derived-alggeom, derived-spaces, infty-topology, a-infinity-algebras (2 currently tagged))

First of the questions about derived algebraic geometry from a noobie.

The way I understand it, every discrete ring R corresponds to some \infty-spectrum whose \pi_0 is R. Now consider p-adic numbers. They are a limit of discrete rings — what should correspond to them? How to generalize?

(+ what could be good tags for derived algebraic geometry? I was considering: e-infinity, infty-structures, math-0703204, derived-alggeom, derived-spaces, infty-topology, a-infinity-algebras (2 currently tagged))