Computing Selmer groups attached to mod p Galois representations

Galois representations
Selmer groups
geometry
cohomology
number theory
grenoble
institut fourier
eem2022

Appears in collection : Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

Selmer groups attached to a p-adic Galois representation have been studied thoroughly, but their mod p cousins have so far received less attention. In this talk we explain the construction of the p-adic Selmer group, how it translates to the mod p setting, and give some progress on understanding the ranks of some Selmer groups over various fields.