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