All Questions

Let $p$ be an odd prime and $\mu_{p}$ be the group of $p^\text{th}$-roots of unity. Then, there exists a cup-product map which maps the product of $p$-copies of $H^{1}(\mathbb{Q}, \mu_{p})$ into $H^{p}...

We know that the motivic cohomology of an abelian variety $A$ over a number field $k$ computes the Mordell-Weil group up to torsion, and so if we were to grant the existence and nice behaviour of ...

Let F be a number field. Does the Hilbert symbols at the various places of F arise from the cup product on the motivic cohomology groups of Spec(F)? And if so, is it possible to interpret Moore's ...