Relative K₀, annihilators, Fitting ideals and the Stickelberger phenomena

2002/03/01 by Victor Snaith, Snaith, Victor
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #math.KT #math.NT

paper · pdf · doi:10.48550/arxiv.math/0203293

arxiv created 2002/03/01 · arxiv updated 2009/12/01

Abstract

When G is abelian and l is a prime we show how elements of the relative K-group K₀(\bf Z_l[G], \bf Q_l) give rise to annihilator/Fitting ideal relations of certain associated \bf Z[G]-modules. Examples of this phenomenon are ubiquitous. Particularly, we give examples in which G is the Galois group of an extension of global fields and the resulting annihilator/Fitting ideal relation is closely connected to Stickelberger's Theorem and to the conjectures Coates-Sinnott and Brumer.

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