Title: An Iwasawa Theoretic Perspective of Chromatic Homotopy Theory

Abstract: We calculate the characteristic polynomials of Iwasawa modules related to height h Morava E-theory over various Iwasawa algebras and use these to prove spectral analogues of a weak form of the Iwasawa Main Conjecture. At height 1, we describe the orders of the K(1)-local homotopy groups of a "torsion-free replacement" of a finite spectrum X in terms of the special values of the characteristic polynomials associated to the p-complete K-theory of X. At height 2, we describe bidegrees of the height shifting spectral sequence, whose abutment is the input of the descent spectral sequence, in terms of the special values of the characteristic polynomials associated to height 2 Morava E-theory. We prove similar results for all heights h>2.

Time: Mar 12, 2026 01:00 PM Eastern Time

In-person location: 1146 Faculty/Administration Building

Zoom link for online audience: https://wayne-edu.zoom.us/j/98258950639?pwd=oxbPJ9AG52epctK14MmNJXOlNV8Z04.1

Meeting ID: 982 5895 0639

Passcode: 715435