Homotopy Theory of A∞ Ring Spectra and Applications to MU-Modules

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On the Adams spectral sequence for R–modules (2001, methodology): “On setting Is = fibre(R −→ R/Is), there is another tower R/I ←− I2 ←− · · · ←− Is ←− Is+1 ←− · · · which is analogous to the external version of [10].”
GALOIS EXTENSIONS OF STRUCTURED RING SPECTRA (2005, methodology): “Our discussion here relies heavily on the work of Maria Basterra [Bas99] and Andrej Lazarev [ La01 ].”
Homology and cohomology of E∞ ring spectra (2004, background): “odules is the category of A-bimodules. When A is coﬁbrant, one typically writes Ae for A ∧ R Aop. More generally, Ae denotes A′ ∧ R A′op, for some ﬁxed choice of coﬁbrant approximation A′ →A. Lazarev [7] identiﬁes Topological Quillen Cohomology in terms of Topological Hochschild Cohomology, and iden”
On differential graded categories (2006, methodology): “Their isomorphism classes in the homotopy category of S-algebras are parametrized by the topological Hochschild cohomology group THH 4 S (Z/2,Z/2) as shown in [97].”
Moduli of objects in dg-categories (2005, methodology): “topically ﬁnitely presented as a B ⊗L Bop-dg-module. But, for any B ⊗L Bop-dg-module M we have MapB⊗LBop−Mod(IB,M) ≃Mapdg−Alg/B(B,B ⊕M), where B ⊕M is the trivial square zero extension of B by M (see [La]). Therefore, the fact that IB is homotopically ﬁnitely presented follows from the fact that B i”