Lübeck's classification of representations of finite simple groups of Lie type and the inverse Galois problem for some orthogonal groups

Zenteno, Adrián

doi:10.1016/j.jnt.2019.06.010

Journal of Number Theory

2020

DOI: 10.1016/j.jnt.2019.06.010

|View full text |Cite

Lübeck's classification of representations of finite simple groups of Lie type and the inverse Galois problem for some orthogonal groups

Adrián Zenteno

Abstract: In this paper we prove that for each integer of the form n = 4̟ (where ̟ is a prime between 17 and 73) at least one of the following groups: PΩ ±

Help me understand this report

View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 13 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Automorphic Galois representations and the inverse Galois problem for certain groups of type 𝐷ₘ

Zenteno

2020

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Let m m be an integer greater than three and ℓ \ell be an odd prime. In this paper we prove that at least one of the following groups: P Ω 2 m ± ( F ℓ s ) \mathrm {P}\Omega ^\pm _{2m}(\mathbb {F}_{\ell ^s}) , P S O 2 m ± ( F ℓ s ) \mathrm {PSO}^\pm _{2m}(\mathbb {F}_{\ell ^s}) , P O 2 m ± ( F ℓ s ) \mathrm {PO}_{2m}^\pm (\mathbb {F}_{\ell ^s}) , or P G O 2 m ± ( F ℓ s ) \mathrm {PGO}^\pm _{2m}(\mathbb {F}_{\ell ^s}) is a Galois group of Q \mathbb {Q} for infinitely many integers s > 0 s > 0 . This is achieved by making use of a slight modification of a group theory result of Khare, Larsen, and Savin, and previous results of the author on the images of the Galois representations attached to cuspidal automorphic representations of G L 2 m ( A Q ) \mathrm {GL}_{2m}(\mathbb {A}_\mathbb {Q}) .

show abstract

Automorphic Galois representations and the inverse Galois problem for certain groups of type 𝐷ₘ

Zenteno

2020

Proc. 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.

Lübeck's classification of representations of finite simple groups of Lie type and the inverse Galois problem for some orthogonal groups

Abstract: In this paper we prove that for each integer of the form n = 4̟ (where ̟ is a prime between 17 and 73) at least one of the following groups: PΩ ±

Cited by 1 publication

References 13 publications

Automorphic Galois representations and the inverse Galois problem for certain groups of type 𝐷ₘ

Automorphic Galois representations and the inverse Galois problem for certain groups of type 𝐷ₘ

Contact Info

Product

Resources

About