On Weil-Stark elements, I: general properties
David Burns, Daniel Macias Castillo, Soogil Seo
TL;DR
This paper introduces a canonical family of elements in the reduced exterior power lattices of global field units, unifying cyclotomic elements in real abelian fields and exploring their arithmetic properties.
Contribution
It constructs a new canonical family of elements that generalizes cyclotomic elements and analyzes their arithmetic properties in global fields.
Findings
Recovers the theory of cyclotomic elements in real abelian fields
Establishes detailed arithmetic properties of the constructed elements
Provides a unified framework for understanding units in global fields
Abstract
We construct a canonical family of elements in the reduced exterior power lattices of the unit groups of global fields. We prove that this family recovers the theory of cyclotomic elements in real abelian fields and also establish detailed arithmetic properties of its elements in the general case.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Coding theory and cryptography · Finite Group Theory Research