Online Talk

Since the 70s it has been expected that the homotopy groups of the rationalization of the K(n)-local sphere are an exterior algebra over the p-adic rationals on classes in degrees 1-2i for i from 1 to n. Recently, Barthel, Schlank, Weinstein and I have discovered a proof of this result by making use of a result of Faltings. In this talk, I will give some background on the K(n)-local sphere, explain the reduction to arithmetic geometry, and then give an idea of the modern techniques in arithmetic geometry that go into the proof.