## Figures from this paper

## 71 Citations

Buildings, elliptic curves, and the K (2)-local sphere

- Mathematics
- 2005

We investigate a dense subgroup Γ of the second Morava stabilizer group given by a certain group of quasi-isogenies of a supersingular elliptic curve in characteristic p. The group Γ acts on the…

On the homotopy of Q(3) and Q(5) at the prime 2

- Mathematics
- 2016

We study modular approximations Q(l), l = 3,5, of the K(2)-local sphere at the prime 2 that arise from l-power degree isogenies of elliptic curves. We develop Hopf algebroid level tools for working…

Topological resolutions in K(2) ‐local homotopy theory at the prime 2

- MathematicsJournal of Topology
- 2018

We provide a topological duality resolution for the spectrum E2hS21 , which itself can be used to build the K(2) ‐local sphere. The resolution is built from spectra of the form E2hF where E2 is the…

TAF and the K(n)-local sphere

- Mathematics
- 2017

These notes are an attempt to understand some of the interesting ideas that take up the later part of Behrens and Lawson’s monograph on topological automorphic forms [3]. In chapters 12 and 13, they…

HOMOTOPY GROUPS OF THE FIBERS OF THE CHROMATIC RESOLUTION OF DETERMINANT TWISTS OF Q(`)

- Mathematics
- 2020

The E(2)-local ring spectrum Q(`) was introduced by Behrens and used in [Beh08] to associate generators βi/j,k of the 2-line of the AdamsNovikov spectral sequence with certain p-adic modular forms…

The homotopy of the K(2)-local Moore spectrum at the prime 3 revisited

- Mathematics
- 2008

In this paper we use the approach introduced in an earlier paper by Goerss, Henn, Mahowald and Rezk in order to analyze the homotopy groups of L_{K(2)}V(0), the mod-3 Moore spectrum V(0) localized…

On the homotopy groups of the K(2)-localisation of a 2-local finite spectrum

- Mathematics
- 2019

Let A1 be any spectrum in a class of finite spectra whose mod-2 cohomology is isomorphic to a free module of rank one over the subalgebra A(1) of the Steenrod algebra. Let EC be the second Morava-E…

MORAVA MODULES AND THE $K(n)$-LOCAL PICARD GROUP

- MathematicsBulletin of the Australian Mathematical Society
- 2015

The chromatic approach to homotopy theory naturally leads to the study of the K(n)local stable homotopy category. In this thesis we study this category in three different ways. The first is to…

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