### Tame torsion of Jacobians and the inverse Galois problem

Linfoot Number Theory Seminar

23rd October 2019, 11:00 am – 12:00 pm

Fry Building, 2.04

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.

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