The Exotic K(2)-Local Picard Group at the Prime 2

2022/12/15 by Agnès Beaudry, Beaudry, Agnes, Irina Bobkova +9
Mathematics · #14C22 #55P42 #55P60 #55Q10 #55Q50 #55Q51 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2212.07858

openalex publication_date 2022/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We calculate the group κ₂ of exotic elements in the K(2)-local Picard group at the prime 2 and find it is a group of order 2⁹ isomorphic to (ℤ/8)² × (ℤ/2)³. In order to do this we must define and exploit a variety of different ways of constructing elements in the Picard group, and this requires a significant exploration of the theory. The most innovative technique, which so far has worked best at the prime 2, is the use of a J-homomorphism from the group of real representations of finite quotients of the Morava stabilizer group to the K(n)-local Picard group.

Related

• The Brown-Comenetz dual of the K(2)-local sphere at the prime 3
• Bounding the K(p-1)-local exotic Picard group at p>3
• On Hopkins' Picard group
• The stable Picard group of A(2)
• Chromatic Picard groups at large primes