Some new perspectives on formal groups

I will talk about (1-dimensional commutative) formal groups, which are an important tool in number theory and topology. In particular, an invariant called "height" determines disjoint classes of formal groups, which in generalized cohomology play roles as different as different prime numbers. However, by a result of Scholze and Weinstein, the classification of formal groups simplifies drastically over large, perfectoid rings, such as the ring of integers of p-adic complex numbers. In particular, over such rings, homomorphisms between formal groups of different heights exist. I  will give some much smaller hands-on examples of this phenomenon, and also explain how these homomorphisms lead to new operations between generalized cohomology theories. This is joint work with P. Hu, D. Kriz, and P. Somberg."