5 problems

Let $Q$ be an anisotropic quadric over $k$, with defining quadratic form $q$, and let $\widetilde{M}_{\operatorname{K}(n)}(Q)$ be its $\operatorname{K}(n)$-kernel motive. Invertibl…

Let $K$ be a compact connected Lie group, $T$ its maximal torus, and $\pi\colon K\rightarrow K/T$ the natural projection. Denote by $G=K_{\mathbb C}$ the corresponding split reduct…

Let $C_d({\mathbb R}^m)$ be the cofiber of the inclusion $\operatorname{Gr}_d({\mathbb R}^{m-1})\hookrightarrow\operatorname{Gr}_d({\mathbb R}^m)$, and let…

Let $n\geq 1$, let $\epsilon$ be $0$ or $1$, and let $l\geq 0$. Set $m=2^{n+1}-\epsilon+2l$, and let $k_n(\operatorname{Gr}_d({\mathbb R}^m))$ denote the dimension of…

Let $BP\langle n\rangle$ denote the Johnson–Wilson spectrum at the prime $2$, with coefficient ring $\mathbb{Z}_{(2)}[v_1,\dots,v_n]$. Assume that $BP\langle n\rangle$ admits the s…