Free Product Decomposition of Galois Groups of Number Fields

Wingberg, Kay

doi:10.2977/prims/1145475355

Publ. Res. Inst. Math. Sci.

2005

DOI: 10.2977/prims/1145475355

|View full text |Cite

Free Product Decomposition of Galois Groups of Number Fields

Kay Wingberg¹

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

On Galois representations with large image

Maire

2023

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

For every prime number p ≥ 3 p\geq 3 and every integer m ≥ 1 m\geq 1 , we prove the existence of a continuous Galois representation ρ : G Q → G l m ( Z p ) \rho : G_\mathbb {Q} \rightarrow Gl_m(\mathbb {Z}_p) which has open image and is unramified outside { p , ∞ } \{p,\infty \} if p ≡ 3 p\equiv 3 mod 4 4 and is unramified outside { 2 , p , ∞ } \{2,p,\infty \} if p ≡ 1 p \equiv 1 mod 4 4 . We also revisit the question of the lifting of residual Galois representations in terms of embedding problems; that allows us to produce Galois representations with open image in the group of upper triangular matrices with diagonal entries equal to 1 1 , unramified outside { p , ∞ } \{p,\infty \} , for m m “small” comparing to p p .

show abstract

On Galois representations with large image

Maire

2023

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Free Product Decomposition of Galois Groups of Number Fields

Cited by 1 publication

References 5 publications

On Galois representations with large image

On Galois representations with large image

Contact Info

Product

Resources

About