All Questions

In his paper "A Hasse principle for function fields over PAC fields" (DOI link), Ido Efrat proves the following result: Let $F$ be an extension of a perfect PAC field $K$ of relative ...

Let $k$ be a field (it is possible to assume that $k = \mathbb{Q}$ or $= \overline{\mathbb{Q}}$) and $X, Y$ nice varieties over $k$. Let $f \colon Y \to X$ be a finite flat surjective morphism of ...

Let $X$ be a locally noetherian regular scheme, and let $Z$ be a closed subscheme of $X$ whose codimension $d > 0$ at every point. Let $U$ be the complement of $Z$ in $X$. For a sheaf $\mathscr{F}$ ...

Let $S$ be a finitely generated domain with the field of fractions $F.$ Let X be a smooth, geometrically connected affine variety over $S.$ Let $A$ be an Azumaya algebra over $X.$ Assume that for all ...

Let $K$ be a field and let $n\geq 2$. If $n=2$, then the set of $K$-isomorphism classes of $PGL_n$-torsors is in bijection with the $n$-torsion of the Brauer group of $K$. Is this only for $n=2$? Is ...

Is etale-Brauer the only obstruction to the existence of rational points on projective plane curves over number fields?