nLab higher chromatic Chern character

Redirected from "higher chromatic Chern characters".
Note: higher chromatic Chern character, higher chromatic Chern character, and higher chromatic Chern character all redirect for "higher chromatic Chern characters".
Contents

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Differential cohomology

Contents

Idea

The traditional Chern character on complex K-theory happens to be a map from complex oriented cohomology theory of chromatic level 1 to one of chromatic level 0 (ordinary cohomology).

More generally, one may ask for higher chromatic Chern characters that map a generalized cohomology theory of some chromatic level to another of some other level.

This has been considered for

References

A survey is for instance in the introduction of

  • Takeshi Torii, Milnor operations and the generalized Chern character, Geom. Topol. Monogr. 10 (2007) 383-421 (arXiv:0903.4708)

  • Takeshi Torii, HKR characters, p-divisible groups and the generalized Chern character, (pdf)

Last revised on July 20, 2017 at 20:39:59. See the history of this page for a list of all contributions to it.