Generalized Etale Cohomology Theories

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Hermitian K-theory, derived equivalences and Karoubi's fundamental theorem (2012, background): “The Tate spectrum Ĥ(G,X) is the homotopy cofibre of the hyper norm map Ñ : XhG → X; see [ACD89], [WW89], [Gre01], [Jar97].”
Cyclic homology, cdh-cohomology and negative K-theory (2005, methodology): “These model structures were studied by Jardine in [19] and [21].”
Toric varieties, monoid schemes and $cdh$ descent (2011, background): “Given a Grothendieck topology, the category of contravariant functors F fromMpctf to spectra (presheaves of spectra) has a closed model structure, in which a morphism φ : F → F ′ is a cofibration when F(X)→ F (X) is a cofibration for every monoid scheme X in Mpctf; φ is a weak equivalence if it indu”