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Unramified Subextensions of Ray Class Field Towers

✍ Scribed by Farshid Hajir; Christian Maire

Book ID
102575837
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
136 KB
Volume
249
Category
Article
ISSN
0021-8693

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✦ Synopsis

Fix a prime l. In this paper, we explore various senses in which the ramification in an infinite l-extension of number fields can be "small." In particular, (1) we construct infinitely many pairs of primes p q (distinct from l) such that admits an infinite l-extension unramified outside p q ; and (2) we explore the possibility of finding infinite unramified subextensions inside infinite ramified l-extensions of number fields.  2002 Elsevier Science (USA)

πŸ“œ SIMILAR VOLUMES

On Quadratic Subextensions of Ray Class
On Quadratic Subextensions of Ray Class Fields of Quadratic Fields mod p
✍ Fuminori Kawamoto πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 290 KB

Let F be a quadratic field and p a prime ideal in F. Then we ask whether the ray class field of F mod p has a normal integral basis over F. We see many differences between our case and the case where the base field F is the field of rational numbers.