Time：14:00-16:00, Wednesday, September 9 2026
Venue：E14-116
Speaker：Yu Kuang, Hainan University
Title：Pro-discrete Iwasawa theory
Abstract: Iwasawa theory is a branch of number theory that studies the behaviour of arithmetic invariants in towers of Galois extensions. Traditionally, the theory is developed after fixing a prime $p$ and working over the $p$-adic Iwasawa algebra $\ZZ_p[[G]]$, so that only the corresponding $p$-primary arithmetic information is retained. Working instead over $\ZZ[[G]]$ allows one to study full arithmetic objects, but these rings are generally neither Noetherian nor naturally compact.
In this talk, I will explain how the theory of pro-discrete modules, introduced by Burns and Daoud, provides a natural framework for addressing these difficulties. I will then discuss recent joint work with David Burns and Dingli Liang concerning the higher coherency properties of completed integral group rings. Finally, I will describe how this framework is used in a recent preprint of Burns to study full divisor class groups and derived Weil–{\'e}tale cohomology of $\mathbb{G}_m$ over $\ZZ_p$-extensions of global function fields, leading to the formulation of a refined version `over $\ZZ$' of the Iwasawa Main Conjecture.
