1.1.3. [0250]
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1.1.3.
Fix an algebraic scheme over , that is, is a scheme of finite type over . Let be the analytification of in the sense of Berkovich [1]. For , the residue field of the associated scheme point of is denoted by . Note that the seminorm at yields an absolute value of . By abuse of notation, it is denoted by . Let be the completion of with respect to . The extension of to is also denoted by the same symbol . The valuation ring of and the maximal ideal of the valuation ring are denoted by and , respectively. Let be an invertible sheaf on . For , is denoted by .