Serre-type conjectures for projective representations

Abstract: We consider automorphy of many representations of the form $\bar \rho:G_K \rightarrow PGL_2(k)$ with $K$ a CM field and $k=F_3,F_5$. In particular we prove (under some mild conditions) that for $F$ totally real, a surjective representation $\bar \rho:G_F \rightarrow PGL_2(F_5)$ with totally odd sign character arises from a Hilbert modular form of weight $(2,\ldots, 2)$. This is joint work with Patrick Allen and Jack Thorne.

number theory

Audience: researchers in the discipline

Upstate New York Online Number Theory Colloquium