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Article

Seven Small Simple Groups Not Previously Known to Be Galois Over Q

Departament de Matemàtiques i Informàtica, University of Barcelona, 08007 Barcelona, Spain
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Academic Editor: Yucai Su
Mathematics 2022, 10(12), 2048; https://doi.org/10.3390/math10122048
Received: 6 April 2022 / Revised: 9 June 2022 / Accepted: 10 June 2022 / Published: 13 June 2022
(This article belongs to the Special Issue New Developments in Number Theory)
In this note we realize seven small simple groups as Galois groups over Q. 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. View Full-Text
Keywords: Galois representations; modular forms; inverse Galois theory; automorphic forms; finite simple groups Galois representations; modular forms; inverse Galois theory; automorphic forms; finite simple groups
MDPI and ACS Style

Dieulefait, L.; Florit, E.; Vila, N. Seven Small Simple Groups Not Previously Known to Be Galois Over Q. Mathematics 2022, 10, 2048. https://doi.org/10.3390/math10122048

AMA Style

Dieulefait L, Florit E, Vila N. Seven Small Simple Groups Not Previously Known to Be Galois Over Q. Mathematics. 2022; 10(12):2048. https://doi.org/10.3390/math10122048

Chicago/Turabian Style

Dieulefait, Luis, Enric Florit, and Núria Vila. 2022. "Seven Small Simple Groups Not Previously Known to Be Galois Over Q" Mathematics 10, no. 12: 2048. https://doi.org/10.3390/math10122048

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