EVENT DETAILS AND ABSTRACT

Title: The rational homotopy groups of the K(n)-local sphere
Speaker: Jared Weinstein
Speaker Info: Boston University
Brief Description:
Special Note:
Abstract:

We compute the rational homotopy groups of the K(n)-local sphere for all heights n and all primes p, verifying a prediction that goes back to Morava in the early 1970s. The key ingredients are (1) the Devinatz-Hopkins spectral sequence, (2) the isomorphism between the Lubin–Tate tower and the Drinfeld tower at the level of perfectoid spaces, (3) integral p-adic Hodge theory, and (4) an integral refinement of a theorem of Tate on the Galois cohomology of non-archimedean fields. This is joint work with Tobias Barthel, Tomer Schlank, and Nathaniel Stapleton.