TL;DR
This paper demonstrates the existence of infinite class field towers for certain number fields ramified at only one prime, expanding understanding of their structure for primes including 2, 3, and 5.
Contribution
It establishes the existence of infinite class field towers for a broad family of primes, including small primes like 2, 3, and 5, in ramified number fields.
Findings
Existence of infinite class field towers for specific ramified number fields.
Construction of such towers for primes 2, 3, and 5.
Advancement in understanding ramification in class field towers.
Abstract
This paper studies infinite class field towers of number fields that are ramified over only at one finite prime. In particular, we show the existence of such towers for a general family of primes including , 3 and 5.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Coding theory and cryptography · Limits and Structures in Graph Theory