An algebraic proof of Brauer's class number formula
Luca Caputo
TL;DR
This paper provides an algebraic proof of Brauer's class number formula by leveraging the Tate exact sequence and regulator constants, offering a new perspective on a classical number theory result.
Contribution
It introduces an algebraic approach to prove Brauer's class number formula using regulator constants and Tate sequences, differing from traditional analytic methods.
Findings
Algebraic proof of Brauer's class number formula
Utilization of Tate exact sequence for units
Application of regulator constants in number theory
Abstract
We show how, starting from the Tate exact sequence for units of Ritter and Weiss, one can obtain an algebraic proof of Brauer's class number formula, using the formalism of regulator constants.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory