What is so 'coloured' on Chromatic Homotopy Theory As the title suggest, I would like know the motivation/ historical background
why  chromatic homotopy theory is called 'chromatic'. Literally, what
analogy to colors it might have.
Accordings to
wikipedia the origin of such homotopy theories bases on
Quillen's work on cohomology theories of formal groups. This allows
due to wikipedia to study that studies complex oriented
cohomology theories from the 'chromatic' point of view.
This involves classification of these theories by so called
'chromatic levels'.
Has this 'visualization' regarding the
theories as 'lying on certain levels' some funny analogy to
colors regarded from physical viewpoint as a part of electromagnetic
spectrum? Sound probably silly but I am quite curious what was the
background for the choice of the name 'chromatic' in this
context.
 A: This term is surely due to Doug Ravenel.  In the mid 1970's, he and collaborators Steve Wilson and Haynes Miller constructed and exploited a "chromatic spectral sequence" for computing Ext groups in the Adams-Novikov spectral sequence.  This is featured in the Doug's book titled Complex cobordism and stable homotopy groups of spheres published in the early 1980s.  As he relates in the intro to that book, he wanted to call it The music of the spheres, but the publisher persuaded him not to.  So chromatic might be more musical than luminary!  At any rate, the term refers to the different sorts of periodicity one finds in stable homotopy: discovered first in the algebra, and then later in actual maps.
The relationship to complex oriented theories is critical.  Quillen wrote his famous paper noting the connection with formal groups.   Jack Morava realized that classification theorems for these proved by number theorists were a guide to cohomology theories that should exist - now called the Morava K-theories - periodic with different periodicies -  and also a guide of how to organize our thinking about stable homotopy.  Miller-Ravenel-Wilson made concrete use of this stuff and Doug was inspired to make his famous conjectures, mainly proved in the mid 1980s by the next generation to come along, ...
