References for the Felix Klein Lectures

Notes

http://www.math.uiuc.edu/~rezk/felix-klein-lectures-notes.pdf

General references

Lecture 1:  A brief introduction to elliptic cohomology: its origin in elliptic genera, and its relation to (derived) algebraic geometry

Lecture 2:  Morava E-theory (generalized cohomology theories associated to universal deformations of formal groups) and its power operations

  • Ando, "Isogenies of formal group laws and power operations in the cohomology theories En", Duke Journal 1995.  The original construction.
  • Ando, Hopkins, Strickland, "The sigma orientation is an H-infinity map", American J. Math 2004.  Describes "descent for level structures", a slightly weaker variant of the "descent for isogenies" described in my talk. http://arxiv.org/abs/math/0204053
  • Rezk, "The congruence criterion for power operations in Morava E-theory", HHA 2009. Gives an outline of the AHS theory of power operations, and describes the role of the "Frobenius congruence". http://arxiv.org/abs/0902.2499
  • Rezk, "Power operations in Morava E-theory: structure and calculations (Draft)". Gives a summary of the theory, and describes some calculations at height 2. http://www.math.uiuc.edu/~rezk/power-ops-ht-2.pdf