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VOL. 58 | 2010 Stability and arithmetic

Abstract

Stability plays a central role in arithmetic. In this article, we explain some basic ideas and present certain constructions for our studies. There are two aspects: namely, general Class Field Theories for Riemann surfaces using semi-stable parabolic bundles and for $p$-adic number fields using what we call semi-stable filtered $(\varphi, N;\omega)$-modules; and non-abelian zeta functions for function fields over finite fields using semi-stable bundles and for number fields using semi-stable lattices.

Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1227.11081
MathSciNet: MR2676162

Digital Object Identifier: 10.2969/aspm/05810225

Rights: Copyright © 2010 Mathematical Society of Japan

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