On units generated by Euler systems

2009/10/08 by Saikia, Anupam
#11R23 #1R18 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0910.1411

Abstract

In the context of cyclotomic fields, it is still unknown whether there exist Euler systems other than the ones derived from cyclotomic units. Nevertheless, we first give an exposition on how norm-compatible units are generated by any Euler system, following work of Coates. Then we prove that the units obtained from Euler systems and the cyclotomic units generate the same ℤ_p-module for any odd prime p. The techniques adopted for the Iwasawa theoretic proof in latter part of this article originated in Rubin's work on main conjectures of Iwasawa theory.

Related

• The Euler system of cyclotomic units and higher Fitting ideals
• Representation of units in cyclotomic function fields
• On the Applications of Cyclotomic Fields in Introductory Number Theory
• On the structure of the module of Euler systems for a p-adic representation
• Notes on the module of Euler systems