6 problems

Let $G=\mathbb{Z}/2$, and consider the classical Tate construction $t_{\mathbb{Z}/2}({\rm inf}^{\mathbb{Z}/2}_{e}(-))^{\mathbb{Z}/2}$. Davis and Mahowald found that it sends the…

Let $G$ be a finite group and $N$ a normal subgroup of $G$. Let $\mathscr{T}_{G,N}(-)$ denote the generalized Tate construction obtained from the relative geometric $N$-fixed point…

Classical blue-shift phenomenon. The spectrum $t_{G}({\rm inf}^G_{e}(E))^G$ is $v_{n-s_{G;E}}$-periodic for some positive integer $s_{G;E}$. When $s_{G;E}>n$, the $v_{n-s_{G;E}}$-p…

Let $y(n)$ and $z(n)/v_n$ be the spectra appearing in the chromatic filtration, and let $(-)^{t\operatorname{\mathbb{T}}}$ denote the Tate construction for the circle group. Write…

Real motivic Tate splitting conjecture. For every $n\geq 1$, the displayed isomorphism holds. The source presents this as an analogue of the preceding motivic splitting conjecture;…

Motivic Tate splitting conjecture. For every $n\geq 1$, the displayed isomorphism holds. This is a weak motivic analogue of a conjecture of Davis and Mahowald; the claimed generali…