This mini course was part the electronic Computational Homotopy Theory Seminar. Videos available the seminar webpage.

Slides

• Part I : Spectra and Localization and the annotated version
• Part II : Complex and the Morava K-Theories and the annotated version
• Part III : The Chromatic Filtration and the annotated version
• Part IV: Morave E-Theory and the Stabilizer Group and the annotated version

Resources

Main reference :

• Ravenel, Nilpotence and Periodicity in Stable Homotopy Theory (also known as the Orange Book)

Other resources:

• Adams, Stable Homotopy and Generalized Homology (no link) (also known as the Blue Book)
• Balmer, A Guide to Tensor-Triangular Classification and The Spectrum of Prime Ideals in Tensor Triangulate Categories
• Barthel, A Short Introduction to the Telescope and Chromatic Splitting Conjectures
• Barthel and Beaudry, Chromatic structures in stable homotopy theory
• Behrens, The Homotopy Groups of L_2S at p greater than or equal to 5
• Bousfield, The localization of spectra with respect to homology
• Dugger, A Geometric Introduction to K-Theory and A Primer on Homotopy Colimits
• Devinatz-Hopkins, Homotopy Fixed Point Spectra for Closed Subgroups of the Morava Stablizer Group
• Goerss, Presheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws
• Hatcher, Vector Bundles and K-Theory
• Hopkins and Smith, Nilpotence and Stable Homotopy Theory II
• Hovey, Operations and Cooperations in Morava E-Theory
• Hovey-Strickland, Morava K-Theories and Localization
• Lurie, Notes on Chromatic Homotopy Theory
• Mathew-Naumann-Noel, Nilpotence and Descent in Equivariant Stable Homotopy Theory
• Margolis, Spectra and the Steenrod Algebra
• Miller, On relations between Adams spectral sequences, with an application to the stable homotopy of a Moore space
• Miller-Ravenel-Wilson, Periodic Phenomena in the Adams-Novikov Spectral Sequence
• Nave, The Smith-Toda Complex V((p+1)/2) does not exist
• Ravenel, Complex Cobordism and the Stable Homotopy Groups of Spheres (also known as the Green Book, even though the latest edition is burgundy)
• Ravenel, Localization with Respect to Certain Periodic Homology Theories
• Rezk, Notes on the Hopkins-Miller Theorem

Places to read about MU: Adams, Part I.2, Lurie's notes, Lecture 5 ... feel free to email me if you have a better suggestion.

Videos on Chromatic Homotopy Theory

In May 2018, CU Boulder hosted a graduate workshop and conference, Chromatic Homotopy Theory: Journey to the Frontier. Videos, notes and exercises are available HERE.

eCHT seminar : An Introduction to Chromatic Homotopy Theory