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

Luis Dieulefait, Enric Florit and Núria Vila
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Luis Dieulefait: Departament de Matemàtiques i Informàtica, University of Barcelona, 08007 Barcelona, Spain
Enric Florit: Departament de Matemàtiques i Informàtica, University of Barcelona, 08007 Barcelona, Spain
Núria Vila: Departament de Matemàtiques i Informàtica, University of Barcelona, 08007 Barcelona, Spain

Mathematics, 2022, vol. 10, issue 12, 1-10

Abstract: 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.

Keywords: Galois representations; modular forms; inverse Galois theory; automorphic forms; finite simple groups (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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