Adelic geometry on arithmetic surfaces I: idelic and adelic interpretation of the Deligne pairing

Paolo Dolce

For an arithmetic surface $X\to B=\mathrm{Spec}{O}_K$ the Deligne pairing $\left <\,,\,\right > \colon \operatorname{Pic}(X) \times \operatorname{Pic}(X) \to \operatorname{Pic…