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2:00pm, Wednesday 17 September

Abstract

Selmer groups are an important construction in modern number theory, with their ranks expected to encode arithmetic information associated to their underlying objects. This is most obvious in conjectures like that of Bloch-Kato, relating an L-value to the rank of a Selmer group of a p-adic Galois representation. In recent years, mod p Galois representations have started to receive similar attention, partly due to Scholze's proof that many torsion classes have their own associated representations. In this talk we will cover some basics of Selmer groups, how to compute them for mod p Galois representations, and how to formulate and test interesting conjectures regarding their ranks.