Let $X$ be a rationally connected variety over an algebraically closed field $k$. Then (1) is the Brauer group $\text{Br}(X)$ finite? (2) is the Picard group $\text{Pic}(X)$ torsion-free?
2026-03-25 03:22:11.1774408931
Finiteness of the Brauer group and torsion-freeness of Picard group of a rationally connected variety over an algebraically closed field
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