The Artin Symbol as a Canonical Capitulation Map
Preda Mihailescu

TL;DR
The paper introduces a canonical, order-preserving map linking class group subgroups to subfields of the Hilbert class field, providing a new perspective on capitulation and a strengthened version of the Hilbert 94 Theorem.
Contribution
It presents a novel, canonical capitulation map that enhances understanding of subgroup structures and capitulation phenomena in Galois number fields.
Findings
Established a canonical map between subgroup lattices
Proved the map is a capitulation map for primes in certain classes
Provided a stronger version of the generalized Hilbert 94 Theorem
Abstract
We show that there is a canonical, order preserving map of lattices of subgroups, which maps the lattice of subgroups of the ideal class group of a galois number field into the lattice of subfields of the Hilbert class field. Furthermore, this map is a capitulation map in the sense that all the primes in the classes of capitulate in . In particular we have a new, strong version of the generalized Hilbert 94 Theorem, which confirms the result of Myiake and adds more structure to (part) of the capitulation kernel of subfields of .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Topology and Set Theory · Rings, Modules, and Algebras
