Stability and Arithmetic

Details Stability and Arithmetic Stability and Arithmetic

2009-04-08

arxiv.org/abs/0904.1337v2

Mathematics

Algebraic Geometry

121 pages

Scientific paper

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

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