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3 votes
0 answers
230 views

A Brauer group of a double covering of a "well-understood" variety

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 ...
k.j.'s user avatar
  • 1,364
1 vote
0 answers
191 views

Vanishing of the local étale cohomology sheaf (?)

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 $\mathscr{F}$ ...
zom's user avatar
  • 185
6 votes
2 answers
516 views

Obstruction and rational points on curves

Is etale-Brauer the only obstruction to the existence of rational points on projective plane curves over number fields?
Pablo's user avatar
  • 11.3k