Mathematical Research Letters
Volume 12, Issue 6, November 2005 pp. 877-884.
A quantitative sharpening of Moriwaki's arithmetic Bogomolov inequalityAuthors: N. Naumann
Author institution: Uni-Regensburg, Denmark
Summary: 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. Soul\'e's proof of a vanishing theorem on arithmetic surfaces.
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