11 problems

Greenlees's conjecture. This map is an isomorphism for all abelian compact Lie groups $A$.

Let $\mathbf{R}$ denote the Real global group law constructed from the Real globally oriented spectrum $\mathbf{MR}$. For each torus $\mathbb{T}^n$, let…

Let $G$ be a compact quasi-abelian Lie group equipped with an augmentation … Write $\rho$ for the relevant regular representation and $M\mathbb{R}_\eta$ for the associated Real equ…

Let $R$ be a regular local ring, and let $\mathrm{MGL}$ denote the motivic Thom spectrum. Consider the $\mathbb{P}^1$-diagonal of the coefficient ring of $\mathrm{MGL}$ over $R$. V…

Uniqueness conjecture. The solution is unique over the universal formal group.

Fix the dihedral group $I_2(m)$ with $m\geq 3$ odd, and let $(R,F)$ be a formal group law such that, for every $\alpha\in\Phi$, … nwhere $p\in R$ is fixed. Let…

Bressler–Evens conjecture. The discovery of this failure of independence deterred further development of the Demazure–Kostant–Kumar line of ideas until work in which the non-indepe…

Let $v\le w$, let … and set $z_i=y_{-\beta_i}$. Let $I_{vw_\circ}$ be a reduced word as above, and let $\ell(v)$ denote the length of $v$. The positivity conjecture. (1) If $t=0$,…

Fix $w e W$ and, for every $vle w$, choose reduced words $I{vwcirc}$ and $Iv'$. Let … be the generating function as an element of $S\otimes_R Q_W$, and let $\mathcal R_w^X$ denote…

Let $\mathcal{F}_{Ab}$ be the universal Abel formal group law, and let its $2$-typization have coefficient ring presented as a quotient of the localized Brown–Peterson coefficient…

Sigma-function coefficient valuation conjecture. The exponents agree: