Let $\mathcal{O}$ be a Dedekind domain and $K = \mathrm{Frac}(\mathcal{O})$ its field of fractions. Let $E / K$ be an elliptic curve and $\mathcal{E} / \mathcal{O}$ its Neron model and $\mathcal{E}^\circ$ the connected component of the identity (fiberwise).


Then the natural map $H^1\_{\mathrm{fppf}}(\mathcal{O}, \mathcal{E}^\circ[n]) \to H^1(K, E[n])$ lands inside $\mathrm{Sel}\_n(E,K) \subset H^1(K, E[n])$. Is there a straightforward description of the kernel and cokernel?



Selmer groups and fppf cohomology
The following paper of Kestutis Cesnavicius answer these and related questions completely: <https://arxiv.org/abs/1301.4724>


