Redshift for truncated Brown-Peterson spectra

Abstract: Ausoni and Rognes calculated that K(ku) has chromatic height 2, at least at primes larger than 3. Their redshift philosophy more generally suggests that the algebraic K-theory of a height n ring spectrum should have height n+1. I will explain work, joint with Dylan Wilson, in which we equip BP(n) with an E_3-BP-algebra structure for all primes p and heights n. The algebraic K-theory of this E_3 ring has chromatic height n+1, giving an example of redshift at arbitrary height. To show the ideas I may present quick proofs, at the prime 2, of the facts that K(ku) is height 2 and K(tmf) is height 3.

algebraic topology

Audience: researchers in the topic

MIT topology seminar

Series comments: We meet at varying times on Monday. Click here to join the zoom meeting . The Zoom meeting room number is 132-540-375.

The mailing list for this seminar is the MIT topology google group. Email Mike Hopkins if you want to join the list.