On a nilpotence conjecture of J.P. May
Speaker: Justin Noel
Speaker organization: University of Regensburg
Abstract:
In 1986 Peter May made the following conjecture:
Suppose that R is a ring spectrum with power operations (e.g., an E_\infty ring spectrum/ commutative S-algebra). Then the torsion elements in the kernel of the integral Hurewicz homomorphism \pi_* R\rightarrow H_* (R;Z) are nilpotent.
If R is the sphere spectrum, this is Nishida's nilpotence theorem. If we strengthen the condition on the integral homology to a condition about the complex bordism of R, then this is a special case of the nilpotence theorem of Devinatz, Hopkins, and Smith.
The proof is short and simple, using only results that have been around since the late 90's. As a corollary we obtain results on the non-existence of commutative S-algebra structures on various quotients of MU. For example MU/(p^i) or ku/(p^i v) for i>0. We also obtain new results about the behavior of the Adams spectral sequence for Thom and THH spectra.
This project is joint with Akhil Mathew and Niko Naumann.
I will fill any remaining time with some fun results about ring spectra with power operations.