### Superelliptic curves with large Galois images

Linfoot Number Theory Seminar

24th March 2021, 4:00 pm – 5:00 pm

Virtual Seminar, https://bristol-ac-uk.zoom.us/j/98122257418?pwd=VXlRdm9RbWNQbmVra3dDTWtLWHpXUT09

Let K be a number field. The inverse Galois problem for K asks if for every finite group G there exists a Galois extension L/K whose Galois group is isomorphic to G. Many people have used torsion points on abelian varieties to realise symplectic similitude groups (GSp_n(F_p)) over Q.

In this talk, we will see how superelliptic curves may be used to realise general linear and unitary similitude groups over cyclotomic fields. A variety of techniques are involved, including those from group theory, CM theory, Odlyzko bounds, and models of curves.

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