Wednesday, March 29, 2023 - 2:30pm
University of Iowa
This is joint work with T. Chinburg and J. Gillibert. The application of Massey products to understand the Galois groups of extensions of number fields is a longstanding research topic. In 2014, Minac and Tan showed that triple Massey products vanish for the absolute Galois group of any field F. In 2019, Harpaz and Wittenberg showed that this remains true for all higher Massey products in the case when F is a number field. The first natural case to consider beyond fields is that of Massey products for curves over fields. I will discuss some known and new vanishing and non-vanishing results in this case. In particular, for elliptic curves I will provide a classification for the non-vanishing of triple Massey products under various natural assumptions. The main tool is the representation theory of etale fundamental groups into upper triangular unipotent matrix groups. I will begin with background about Massey products, which first arose in topology, and about the relevant representation theory, before discussing our results.