Reflection theorems for number rings
Evan M. O'Dorney
TL;DR
This paper discusses reflection theorems related to number rings, presenting foundational lemmas and results that underpin more advanced findings in the field of algebraic number theory.
Contribution
It provides elementary lemmas and foundational proofs that support the main reflection theorems for number rings, serving as a basis for subsequent research.
Findings
Elementary lemmas for number rings
Reflection theorems established
Supporting proofs for advanced results
Abstract
This is the original version of my Ph.D. thesis. The main results have been divided up between papers arXiv:2111.09784 and arXiv:2204.10924. This paper has been kept on the arXiv to preserve some proofs of elementary lemmas that will be removed from the peer-reviewed version.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Mathematical Identities · Advanced Algebra and Geometry