Arithmetic Linear Series with Base Conditions
نویسنده
چکیده
In this note, we study the volume of arithmetic linear series with base conditions. As an application, we consider the problemof Zariski decompositions on arithmetic varieties. Introduction LetXbeaprojective andflat integral schemeoverZ. Weassume thatX is normal and thegeneric fiber ofX → Spec(Z) is a d-dimensional smoothvariety overQ. Let Div(X) be the groupofCartier divisors onX and letDiv(X)R := Div(X)⊗ZR. Apair D = (D, g) is called an arithmetic R-Cartier divisor of C0-type if D ∈ Div(X)R (i.e. D = ∑r i=1 aiDi for someD1, . . . ,Dr ∈ Div(X) and a1, . . . , ar ∈ R), g : X(C) → R∪{±∞} is a locally integrable function invariant under the complex conjugation map F∞ : X(C) → X(C) and, for any point x ∈ X(C), there are an open neighborhood Ux of x and a continuous function ux over Ux such that
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تاریخ انتشار 2017