nLab Chromatic Homotopy Theory





Special and general types

Special notions


Extra structure



Stable Homotopy theory

Higher algebra

This page collects links related to the lecture notes

on complex oriented cohomology, the Adams spectral sequence and chromatic homotopy theory from the modern point of view of E-infinity geometry.

Based on the program of

as nicely laid out in more detail in

First indications of the big picture developed here are due to

Via the chromatic stratification of the moduli stack of formal groups one recovers as, roughly, the second chromatic stage the moduli stack of elliptic curves. For the story in that case see

See also



Lecture 1 Introduction

Lecture 2 Lazard’s theorem

Lecture 3 Lazard’s theorem (continued)

Lecture 4 Complex-oriented cohomology theories

Lecture 5 Complex bordism

Lecture 6 MU and complex orientations

Lecture 7 The homology of MU

Lecture 8 The Adams spectral sequence

Lecture 9 The Adams spectral sequence for MU

Lecture 10 The proof of Quillen’s theorem

Lecture 11 Formal groups

Lecture 12 Heights and formal groups

Lecture 13 The stratification of FG\mathcal{M}_{FG}

Lecture 14 Classification of formal groups

Lecture 15 Flat modules over FG\mathcal{M}_{FG}

Lecture 16 The Landweber exact functor theorem

Lecture 17 Phantom maps

Lecture 18 Even periodic cohomology theories

Lecture 19 Morava stabilizer groups

Lecture 20 Bousfield localization

Lecture 21 Lubin-Tate theory

Lecture 22 Morava E-theory and Morava K-theory

Lecture 23 The Bousfield Classes of E(n)E(n) and K(n)K(n)

Lecture 24 Uniqueness of Morava K-theory

Lecture 25 The Nilpotence lemma

Lecture 26 Thick subcategories

Lecture 27 The periodicity theorem

Lecture 28 Telescopic localization

Lecture 29 Telescopic vs E nE_n-localization

Lecture 30 Localizations and the Adams-Novikov spectral sequence

Lecture 31 The smash product theorem

Lecture 32 The chromatic convergence theorem

Lecture 33 Complex bordism and E(n)E(n)-localization

Lecture 34 Monochromatic layers

Lecture 35 The image of JJ

category: reference

Last revised on January 2, 2021 at 16:23:09. See the history of this page for a list of all contributions to it.