Matthew Bisatt

Tame torsion of Jacobians and the inverse Galois problem

Fix a positive integer g and prime p. Does there exist a curve of genus g, defined over the rationals, such that the mod p representation of its Jacobian is everywhere tamely ramified? In other words, can we make the ramification of the p-torsion points as nice as possible?

We will approach this question via the theory of Mumford curves and give an application to a variant of the inverse Galois problem. This is joint work with Tim Dokchitser.