Inequality of Bogomolov-Gieseker's type on arithmetic surfaces
Abstract
Let K be an algebraic number field, OK the ring of integers of K, and f : X --> Spec(OK) an arithmetic surface. Let (E, h) be a rank r Hermitian vector bundle on X such that E is semistable on the geometric generic fiber of f. In this paper, we will prove an arithmetic analogy of Bogomolov-Gieseker's inequality: c2(E, h) - (r-1)/(2r) c1(E, h)2 >= 0.
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