# Research Seminar: Higher Chern classes in Iwasawa theory

In this seminar, we mainly follow the paper “Higher Chern classes in Iwasawa theory” by Bleher, Chinburg, Greenberg, Kakde, Pappas, Sharifi, and Taylor.

We study the higher codimension behavior of Iwasawa modules. Classical main conjectures can be interpreted as saying that the first Chern class of an Iwasawa module (the characteristic ideal) is given by a $p$-adic $L$-function. First Chern classes describe the codimension one behavior of modules. A conjecture by Greenberg asserts that the first Chern classes of various natural Iwasawa modules vanish. This leads to the idea that to obtain a better insight into the structure of an Iwasawa module, one needs to study its higher codimension behavior, given by higher Chern classes.

We will mainly focus on the case of CM-fields and, in particular, on the Iwasawa theory over imaginary quadratic fields, where an odd prime $p$ splits.

Program: pdf

Date Title Speaker
30.04.2020 Introduction (pdf) Andreas Nickel
07.05.2020 $K_2$ of a ring (pdf) Ran Azouri
14.05.2020 Matsumoto’s theorem and higher Chern classes (pdf) Xiaoyu Zhang
28.05.2020 Generalities on Iwasawa theory (pdf) Gürkan Dogan
04.06.2020 Duals of Iwasawa modules Andreas Bode
18.06.2020 Spectral sequences and the core diagram
25.06.2020 Some consequences of Leopoldt’s conjecture Antonio Mejías Gil
02.07.2020 Reflection-type theorems for Iwasawa modules Luca Dall’Ava
09.07.2020 Katz $p$-adic $L$-functions and proof of the main result Nils Ellerbrock
16.07.2020 Program discussion for next term