7 problems

Let $k$ be a number field and let $C/k$ be a smooth projective curve. The information obtained from finite abelian descent is said to cut out precisely the rational points if the c…

Let $k$ be a number field, and let $\mathcal X$, $\mathcal Y$, and $\mathcal Z$ be algebraic $k$-stacks. Let $F$ and $G$ be linear $k$-groups, and let … be torsors. Torsor covering…

Let $k$ be a global field, let $A$ be an abelian variety over $k$, and let $X\subset A$ be a smooth closed subvariety. Write $X(\mathbb{A}_k)_\bullet^{\operatorname{Br}}$ for the B…

Let $C$ and $D$ be smooth, proper and geometrically integral curves over a finite field ${\mathbb F}$, and let $K:= {\mathbb F}(D)$. Write $C$ for the base change…

Let $k$ be a number field and let $X/k$ be a variety with $X(k)=\emptyset$. A stratification of $X$ is a decomposition … For each stratum, let $\cl{X_i}$ be its closure and let…

Let $k$ be a number field and let $\poneminusthreepoints_k$ denote the thrice-punctured projective line over $k$. VSA for $(\fab,f,k)$ is the finite abelian descent property used i…

Let $k$ be a number field. A variety satisfies VSA for $(\fab,f,k)$ if the corresponding finite abelian descent obstruction has the stated property of the paper. Finite abelian des…