\(K\) of mixed characteristic \((0,p)\) means that \(K\) has characteristic 0, but its residue field \(\kappa\) has characteristic \(p\))
Mixed characteristic
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Fargues-Fontaine Reading Notes
Mixed characteristic : a ring \(R\) with an ideal \(I{~\trianglelefteq~}R\) with \(\operatorname{ch}R = 0\) but \(\operatorname{ch}R/I = p > 0\). The motivating examples: \({\mathbb{Z}}\), or \({\mathcal{O}}_K\) for \(K\) a number field, \({ {\mathbb{Z}}_p }\).