TL;DR
This paper introduces index-modules for A-lattices in vector spaces over Dedekind rings and uses this concept to prove a weak Gras conjecture for Stark units in global function fields.
Contribution
It defines index-modules for A-lattices and applies this to provide an elementary proof of a weak Gras conjecture in the context of global function fields.
Findings
Proved the weak Gras conjecture for Stark units in global function fields.
Introduced the concept of index-modules for A-lattices.
Provided an elementary proof technique for the conjecture.
Abstract
We define the notion of index-module for a couple of A-lattices in a vector space, A being a Dedekind ring. We apply this notion to prove by elementary means that a weak Gras conjecture (i.e for irreducible nontrivial Q-characters) holds for a suitable group of Stark units in global function fields.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Rings, Modules, and Algebras · Algebraic structures and combinatorial models