$PGL_2(\mathbb{F}_\ell)$ number fields with rational companion forms
David P. Roberts
TL;DR
This paper provides a comprehensive list of fifty-three $PGL_2( _ell)$ number fields with rational companion forms for primes $ell \,\geq\, 11$, highlighting their ramification properties.
Contribution
It presents what appears to be a complete list of such number fields, including some with minimal ramification, advancing understanding of their structure and properties.
Findings
List of 53 $PGL_2( _ell)$ number fields with rational companion forms.
Some fields are very lightly ramified for their Galois group.
The list is likely complete.
Abstract
We give a list of number fields for which have rational companion forms. Our list has fifty-three fields and seems likely to be complete. Some of the fields on our list are very lightly ramified for their Galois group.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology