Lubin-Tate theory, character theory, and power operations

@article{Stapleton2020LubinTateTC,
  title={Lubin-Tate theory, character theory, and power operations},
  author={Nathaniel J. Stapleton},
  journal={Handbook of Homotopy Theory},
  year={2020}
}
  • N. Stapleton
  • Published 29 October 2018
  • Mathematics
  • Handbook of Homotopy Theory
This expository paper introduces several ideas in chromatic homotopy theory around Morava's extraordinary E-theories. In particular, we construct various moduli problems closely related to Lubin-Tate deformation theory and study their symmetries. These symmetries are then used in conjunction with the Hopkins-Kuhn-Ravenel character theory to provide formulas for the power operations and the stabilizer group action on the E-cohomology of a finite group. 
5 Citations

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References

SHOWING 1-10 OF 22 REFERENCES

The character of the total power operation

In this paper we compute the total power operation for the Morava $E$-theory of any finite group up to torsion. Our formula is stated in terms of the $GL_n(Q_p)$-action on the Drinfeld ring of full

GENERALIZED GROUP CHARACTERS AND COMPLEX ORIENTED COHOMOLOGY THEORIES

Let BG be the classifying space of a finite group G. Given a multiplicative cohomology theory E ⁄ , the assignment G 7i! E ⁄ (BG) is a functor from groups to rings, endowed with induction (transfer)

H Ring Spectra and Their Applications

Extended powers and H? ring spectra.- Miscellaneous applications in stable homotopy theory.- Homology operations for H? and Hn ring spectra.- The homotopy theory of H? ring spectra.- The homotopy

Notes on the Hopkins-Miller theorem

We give an exposition of the proof of a theorem of Hopkins and Miller, that the spectra En admit an action of the Morava stabilizer group.

Formal moduli for one-parameter formal Lie groups

L’acces aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html), implique l’accord avec les conditions generales d’utilisation

The sigma orientation is an H∞ map

<abstract abstract-type="TeX"><p>In an earlier paper, the authors constructed a natural map, called the <i>sigma orientation</i>, from the Thom spectrum <i>MU</i> <6> to any elliptic spectrum.