7 problems

Let $F$ be a real closed field, and write $\operatorname{DATM}_{\operatorname{gm}}(F;\mathbb{Q})$ for the triangulated category of geometric Artin–Tate motives over $F$ with ration…

Let $\FF$ be a general real closed field, and consider the canonical comparison map … The fiber above the generic point of $\Spec(\bbZ)$ is the fiber whose structure is undetermine…

Effectivity conjecture. The groups $\operatorname{CWH}^j_{i,K}(M)$ are finite-dimensional $\mathbb{Q}$-vector spaces for every $(i,j)\in I$ if and only if $M$ belongs to the extens…

Let $l$ be prime, let $k={\mathbb Z}/l$, and let $M/K$ be a cyclic extension of degree $l$ of fields containing a primitive $l$th root of unity. Assume the Milnor–Bloch–Kato conjec…

Let $k={\mathbb Q}$, let $K$ be a field with $\operatorname{char}K=p\ne0$, let $M/K$ be a Galois extension, and let $k[L']$ and $k[L”]$ denote the motives of finite intermediate ex…

Let $k$ be one of ${\mathbb Z}$, ${\mathbb Q}$, ${\mathbb Z}[m^{-1}]$, or ${\mathbb Z}/m$ with $m\ge2$, let $K$ be a field, and let $M/K$ be a Galois extension. Let ${\mathcal D}$…

Let $k$ be one of ${\mathbb Z}$, ${\mathbb Q}$, ${\mathbb Z}[m^{-1}]$, or ${\mathbb Z}/m$ with $m\ge2$, and let $K$ be a field. Let $M/K$ be a finite Galois extension, let…