8 problems

Let $F$ be a field, and let $\mathrm{SH}_F$ denote the motivic stable homotopy category over $F$. Let $\mathrm{MGL}$ be the algebraic cobordism spectrum, let $a_i$ be generators of…

Let $S\in\mathrm{Rg}$ be a base ring, let $\mathrm{MS}_{\mathrm{Nis}}(S)$ denote the Nisnevich motivic stable category over $S$, and let $\mathbf{MGL}$ be the algebraic cobordism s…

Let $S\in\mathrm{Rg}$ be a base ring, and let $\mathrm{SH}(S)$ denote the stable motivic homotopy category over $S$. Let $\mathbf{MGL}\in\mathrm{SH}(S)$ be the algebraic cobordism…

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 $A$ be a local Noetherian ring. Write $d53f^*$ for the Lazard ring with cohomological grading. Lazard-ring computation conjecture. The natural map … is an isomorphism. This con…

Let $k$ be a field, let $\bMGL$ denote the motivic algebraic cobordism spectrum, let $\bT$ be the motivic suspension coordinate, and let $\bDM(k)$ be the category of motives over…

Algebraic cobordism torsion-freeness conjecture.

Let $X$ be a smooth variety of dimension $d$. A free ${\mathbb{L}}$-resolution of $\Omega^*(X)$ is one whose $j$-th term has generators concentrated in codimensions between $j$ and…