@pro: when people say that spectra aren't the same as cohomology theories, they're talking about cohomology theories regarded as taking values in graded abelian groups. denis' description of spectra involves lifts of these (co)homology theories to theories taking values in spaces (which will then in fact be infinite loop spaces)
you get back to graded abelian groups by taking homotopy groups. the badness of this construction (e.g. the fact that it allows phantom maps to exist) comes from the fact that taking homotopy groups is not a faithful functor
this is a bit curious because by whitehead's theorem taking homotopy groups is a conservative functor. examples of conservative functors that aren't faithful are a bit hard to come by because they're ruled out by mild hypotheses that happen not to hold here
@lenticcatachresis I remember trying to use this at some point and getting very confused about it. I THINK that maybe @EricPeterson figured it out? I can't remember.
oh. That's nonsense. What I've been doing (since yesterday) is make a bookmark, then save the bookmark page as an html in my computer, then delete the bookmark
Can I ask you a dumb question. In Katz Mazur they claim that the "disjoint union of the legendre family and naive level three structure is an etale cover of M_{1,1}"
Why is it that the Legendre family alone is not a cover? (Let's work over $\Bbb{C}$)
After all every family of elliptic curves $X \to S$ etale locally on $S$ acquires a Legendre form.
