Sets of Completely Decomposed Primes in Extensions of Number Fields

TL;DR

This paper introduces the concept of saturated prime sets in number fields and proves an analogue of Riemann's existence theorem for their decomposition groups, advancing understanding of prime decomposition in algebraic extensions.

Contribution

It defines saturated prime sets and establishes a Riemann existence theorem analogue for their decomposition groups in infinite extensions.

Findings

Introduction of saturated prime sets in number fields

Proof of Riemann existence theorem analogue for these sets

Extension of prime decomposition theory in algebraic number fields

Abstract

We introduce the notion of saturated sets of primes of an algebraic number field and prove an analogue of Riemann's existence theorem for the decomposition groups of infinite stably saturated sets of primes.