Galois representations into $G_2$ and lattice constructions

Abstract: I will describe some recent work in progress on the symmetric cube Bloch-Kato conjecture, constructing elements in certain symmetric cube Selmer groups. This work goes by $p$-adically deforming Eisenstein series on the exceptional group $G_2$ in a cuspidal family, and taking Galois representations associated with the members of this family. I will describe what one must do on the Galois side to make this method work.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar