Advanced Studies in Pure Mathematics

Stability and arithmetic

Lin Weng

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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.

Article information

Source
Algebraic and Arithmetic Structures of Moduli Spaces (Sapporo 2007), I. Nakamura and L. Weng, eds. (Tokyo: Mathematical Society of Japan, 2010), 225-359

Dates
Received: 25 March 2009
Revised: 5 August 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086133

Digital Object Identifier
doi:10.2969/aspm/05810225

Mathematical Reviews number (MathSciNet)
MR2676162

Zentralblatt MATH identifier
1227.11081

Citation

Weng, Lin. Stability and arithmetic. Algebraic and Arithmetic Structures of Moduli Spaces (Sapporo 2007), 225--359, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05810225. https://projecteuclid.org/euclid.aspm/1543086133


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