Ando, Morava, and Sadofsky showed that the Tate construction for a trivial Z/p-action decreases the chromatic height of Johnson-Wilson theory, and Greenlees and Sadofsky proved that the Tate construction for a trivial finite group action vanishes on Morava K-theory. We prove C 2equivariant enrichments of these results using the parametrized Tate construction. The C 2 -fixed points of our results produce new blueshift and vanishing results for Real Johnson-Wilson theories ER(n) and Real Morava K-theories KR(n), respectively, for all n. In particular, our blueshift results generalize Greenlees and May's Tate splitting of KO to all chromatic heights.

No abstract

No abstract

We analyze the C-motivic (and classical) Adams-Novikov spectral sequence for the C-motivic modular forms spectrum mmf (and for the classical topological modular forms spectrum tmf ). We primarily use purely algebraic techniques, with a few exceptions. Along the way, we settle a previously unresolved detail about the multiplicative structure of the homotopy groups of tmf .