I am reading Bousfield's paper entitled "The localization of spectra with respect to homology" (MSN). In that paper, Corollary 6.13 states that, if a ring spectrum $E$ with countable homotopy and satisfies some vanishing conditions in the associated Adams spectral sequence, then the localization is equivalent to nilpotent completion.

So, my question is the following:

What are the ring spectra $E$ (I need an updated list) satisfying the above conditions?

I am reading Bousfield's paper entitled "The localization of spectra with respect to homology" (MSN). In that paper, Corollary 6.13 states that, if a ring spectrum $E$ has countable homotopy and satisfies some vanishing conditions in the associated Adams spectral sequence, then the localization is equivalent to nilpotent completion.

So, my question is the following:

What are the ring spectra $E$ (I need an updated list) satisfying the above conditions?

I am reading Bousfield's paper entitled "The localization of spectra with respect to homology. " In that paper, Corollary 6.13 states that if a ring spectrum E with countable homotopy and satisfies some vanishing conditions in the associated Adams spectral sequence then the localization is equivalent to nilpotent completion.

So, my question is the following. What are the ring spectra E ( I need an updated list) satisfying above conditions?

Thank you so much in advance.

I am reading Bousfield's paper entitled "The localization of spectra with respect to homology" (MSN). In that paper, Corollary 6.13 states that, if a ring spectrum $E$ with countable homotopy and satisfies some vanishing conditions in the associated Adams spectral sequence, then the localization is equivalent to nilpotent completion.

So, my question is the following:

What are the ring spectra $E$ (I need an updated list) satisfying the above conditions?