Number Theory Seminar

Speaker: Angelot Behajaina (Universite de Caen Normandie)

Title: The Inverse Galois Problem over twisted skew fields of rational fractions

Abstract: The inverse Galois problem over a field K asks whether every finite group is a Galois group over K. Traditionally, the inverse Galois problem is studied over fields. However, the notion of Galois extensions exists in the noncommutative setting. In 2019, Bruno Deschamps and François Legrand proved that the inverse Galois problem had a positive answer over the twisted skew field H(T) of rational fractions with central indeterminate, where H is a skew field of finite dimension over its center k containing an ample field. In this talk, I present a generalization of the result of Deschamps and Legrand to twisted skew fields H(T,σ) of rational fractions where H is not necessarily of finite dimension over its center and σ is any automorphism of finite order of H. Moreover, a similar result for infinite profinite groups will be discussed

The talk will take place on Zoom. If you would like to receive the Zoom link and are not part of our current NT Seminar mailing list, please contact the organizer.