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. 
[PDF] Semantic Reader
5 Citations

5 Citations

Lecture 16: Character isomorphisms via tempered cohomology

These are extended notes from a talk at the 202One Talbot Workshop on Ambidexterity. Their purpose is to explain how to use Lurie’s work on elliptic cohomology to recover character isomorphisms in…

Chromatic structures in stable homotopy theory

In this survey, we review how the global structure of the stable homotopy category gives rise to the chromatic filtration. We then discuss computational tools used in the study of local chromatic…

Level structures on $p$-divisible groups from the Morava $E$-theory of abelian groups

The close relationship between the scheme of level structures on the universal deformation of a formal group and the Morava $E$-cohomology of finite abelian groups has played an important role in the…

$E_n$ ring spectra and Dyer-Lashof operations

This is an expository article about power operations and their connection with the study of highly structured ring spectra. In particular, we discuss Dyer-Lashof operations and their evolving role in…

Additive power operations in equivariant cohomology

Let $G$ be a finite group and $E$ be an $H_\infty$-ring $G$-spectrum. For any $G$-space $X$ and positive integer $m$, we give an explicit description of the smallest Mackey ideal $\underline{J}$ in…

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…

Finite subgroups of formal groups

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.…

Maps between classifying spaces. II

H∞ RING SPECTRA AND THEIR APPLICATIONS (Lecture Notes in Mathematics 1176)

Maps between classifying spaces