Timeline for Finiteness of the Brauer group for flat proper schemes over $\operatorname{Spec} \mathbf{Z}$
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2017 at 6:29 | comment | added | user19475 | Yes, I forgot the infinite places. | |
| Nov 25, 2017 at 5:04 | comment | added | user87684 | This is true when $X$ is a smooth projective curve over a finite field by a Thm of Grothendieck, and if $X$ is smooth projective geometrically irreducible over a finite field by fairly elementary arguments, but it's not quite true if $X$ is the spectrum of the ring of integers of an algebraic number field $K$. $\text{Br}(\mathscr{C})$ should surject onto $H^1(X_{\rm\acute{e}t}, \text{Pic}^0_{\mathscr{C}/X})$ (actually onto its image into $H^1(X_{\rm\acute{e}t}, \text{Pic}_{\mathscr{C}/X})$, which is off from the Tate-Shafarevich group by a finite group of exponent $2$ if $K$ has a real place.) | |
| Nov 7, 2017 at 15:21 | history | answered | user19475 | CC BY-SA 3.0 |