Sourayan Banerjee

Relative Brauer groups and Kummer Sequence without characteristic constraint in $fppf$-topology

Let $f: X\rightarrow S$ be a faithful affine map. In this article we construct a group homomorphism $\theta_{{fppf}}: \text{Br}(f) \longrightarrow H^1_{{fppf}}\!\left(S, (f_*\mathcal{O}_X^\times / \mathcal{O}_S^\times)_{{fppf}}\right)$, extending the formerly defined morphism over an \'etale site $\theta_{et}$. In doin...