

Chromatic Phenomena in Stable Homotopy Theory

The central object of study in
stable homotopy theory
is
the stable homotopy groups of spheres
. They are simpler than unstable counter parts, but
still very hard to study.
Thanks to Quillen’s work
[
Qui69
]
, we know
the complex cobordism
MU
and its
p
local summand
BP
are useful in the study of stable homotopy theory.
Namely, periodicities with respect to the generators
v
_{
n
}
in the coefficient ring of
BP
are the key.
This is made explicit by Ravenel
[
Rav84
]
. Ravenel’s conjectures, studied mainly by
Hopkins and his collaborators, are the driving force
for the developement of stable homotopy theory in 90s.
Although stable rational homotopy theory is almost
(graded) linear algebra over
ℚ
, there are interesting facts when we allow group
actions as is said by Greenlees in
[
Gre
]
.


