Superelliptic curves with large Galois images

Abstract: 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 (${\rm GSp}_n(F_\ell)$) over $Q$.

In this talk, we examine mod $\ell$ Galois representations attached to superelliptic curves and use them to realise general linear and unitary similitude groups over cyclotomic fields. A variety of mathematics is involved, including group theory, CM theory, root discriminant bounds, and models of curves.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html