7 problems

Weak abelian-variety conjecture. There exists $W$ such that

Let $A$ act on the motive $M$, and let $W$ be an $A$-submodule of $H^{i+1}_{\mathcal{M}/\mathcal{O}_K}(M,E(n))$. Let $r_{\mathrm{B}}$ be the Beilinson regulator, and suppose … Let…

Let $A$ be the semisimple coefficient algebra acting on the motive $M$, let $d$ be its relevant dimension, let $i$ be an integer, and let $n>\frac{i}{2}+1$ be an integer. For an em…

Let $A$ be the semisimple coefficient algebra acting on the motive $M$, let $i$ be an integer, and let $n>\frac{i}{2}+1$ be an integer. Write $L({}_A H^i(M),n)$ for the equivariant…

Let $K/k$ be a finite Galois CM-extension with Galois group $G$. Let $S$ contain all ramified finite places and all infinite places of $k$, let…

Let $L/K$ be a Galois CM-extension with Galois group $G$. Let $S$ be a finite set of places of $K$ containing all ramified and infinite places. For $\alpha\in L^\times$, define…

Let $L/K$ be a Galois extension with Galois group $G$. Assume that $S$ contains all infinite and ramified places of $K$, that $S$ is disjoint from a finite set $T$ of places, and t…