Week 1: Iwasawa theory over function fields
Schedule overview (March 23 - 27, 2026)
(all talks at ICMAT’s Aula Naranja)
Mini Courses
Title: Iwasawa theory for ordinary semistable elliptic curve over function fields of characteristic \(p>0\)
- Speakers: Ki-Seng Tan (Taiwan National University) and Fabien Trihan (Sophia University, Japan).
- Abstract: Let \(A/K\) be a semistable ordinary elliptic curve over a global function field of characteristic \(p>0\). Let \(L/K\) be a \(\mathbf{Z}_p^d\)-extension ramified at finitely many places, either of good ordinary reduction for \(A/K\) or of multiplicative reduction. Our talk will present both foundational and recent results around the Iwasawa theory of \(A\) over \(L/K\).
Title: On equivariant refinement of BSD conjecture over global function fields
- Speakers: Wansu Kim (KAIST)
- Abstract: The aim of the lecture series is to explain the formulation of the equivariant BSD conjecture over global function fields, following the joint work with D. Burns and M. Kakde. Along the way, we will review the necessary backgrounds in abelian varieties, homological algebra, and group theory.
Standalone talks
Title: Stickelberger series for divisor class groups of function fields
- Speakers: Andrea Bandini (Università degli Studi di Pisa)
- Abstract: We consider the Iwasawa module of classes of divisors of degree zero in a pro-p-extension of a function field of characteristic p. We define a Stickelberger series and show that it provides the analytic counterpart of characteristic ideals for the p-part of that module in the Carlitz cyclotomic extension, thus proving an Iwasawa Main Conjecture (IMC) for this setting (joint work with B. Anglès, F. Bars and I. Longhi).
For the l-part of the same module (l a prime different from p), we present an algebraic approach to the structure of modules over the appropriate Iwasawa algebra. This structure, together with the same Stickelberger series defined for the p-parts, allows us to formulate (and prove some special cases of) an IMC for this setting (joint work with I. Longhi).
Title: Iwasawa theory over Drinfeld modular towers
- Speakers: Maxim Mornev (UCM-ICMAT)
- Abstract: We formulate and prove an Iwasawa main conjecture for \(\mathbb{G}_m\) over division fields arising from Drinfeld modules and, more generally, from abelian Anderson modules. This is joint work in progress with David Burns and Daniel Macías Castillo.