Seven Small Simple Groups Not Previously Known to Be Galois Over <inline-formula><math display="inline"><semantics><mi mathvariant="double-struck">Q</mi></semantics></math></inline-formula>
In this note we realize seven small simple groups as Galois groups over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">Q</mi></semantics></math></i...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/12/2048 |
| Summary: | In this note we realize seven small simple groups as Galois groups over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">Q</mi></semantics></math></inline-formula>. The technique that we employ is the determination of the images of Galois representations attached to modular and automorphic forms, relying in two cases on recent results of Scholze on the existence of Galois representations attached to non-selfdual automorphic forms. |
|---|---|
| ISSN: | 2227-7390 |