# Algebra/Number Theory Seminar

## Serre-type conjectures for projective representations

Chandrashekhar Khare, UCLA

Monday, June 8th, 2020
12:00 PM - 1:00 PM
Upstate NY online Number Theory colloquium, researchseminars.org

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 $(2,\ldots, 2)$.

Event contact: dinesh dot thakur at rochester dot edu