2005/08/31 by Niko Naumann, Naumann, Niko
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0508641
final version, to appear in Math. Res. Lett
arxiv created 2005/08/31 · arxiv updated 2009/12/01
A. Moriwaki proved the following arithmetic analogue of the Bogomolov unstability theorem. If a torsion-free hermitian coherent sheaf on an arithmetic surface has negative discriminant then it admits an arithmetically destabilising subsheaf. In the geometric situation it is known that such a subsheaf can be found subject to an additional numerical constraint and here we prove the arithmetic analogue. We then apply this result to slightly simplify a part of C. Soulé's proof of a vanishing theorem on arithmetic surfaces.