A quantitative sharpening of Moriwaki's arithmetic Bogomolov inequality
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Publication:812533
DOI10.4310/MRL.2005.V12.N6.A8zbMATH Open1110.14023arXivmath/0508641MaRDI QIDQ812533
Author name not available (Why is that?)
Publication date: 24 January 2006
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/math/0508641
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